Capital is one of the defining concepts of the 21st century.
The American Heritage Dictionary (4th Ed.) offers the narrow definition of “Wealth, especially in the form of financial or physical assets, used in the production or accumulation of more wealth.” Its broader definition is “Accumulated assets or advantages used for economic or political gain.” The word comes from the Latin capitālis, from caput, “head” or “money laid out.”  People who have capital get to direct materials, labor, culture, organizations, ideas, and more.
I think of capital in computer science terms: a generator that’s a routine that can be used to control the iteration behavior of a loop.  In economic terms, that means increasing returns to wealth; a small bit replicates itself over time. It’s one of the defining characteristics of living organisms to create capital, which helps life grow, expand, and thrive.
Types of Capital
When people think of capital, they too often focus on “money” or “financial assets” and not the more important versions of it. Below I state and rank capital from the least important to most (the first three form a group on stuff, the fourth to seventh form a group around people, ideas, society, and institutions).
1. Financial assets: cash, checks, stocks, bonds, deeds, derivatives, bitcoin, NFTs, etc.
2. Physical, manufactured capital: tools, buildings, bridges, roads, computers, and telecommunications assets.
3. Natural resources: land, water, air, forests, beaches, steel, agricultural products, oil, coal, sunlight, and climate.
4. Institutional capital: local, state, and federal governments; democracy and human rights; legal protections of tangible and intangible property; firms that maximize value to stakeholders (serve customers, compensate and train workers, create value for shareholders); schools, universities, and think tanks; NGOs; religious organizations like churches, mosques, etc. Institutions exist to promote cooperation and align incentives. 
5. Intellectual capital: books, international patents, languages, philosophy, religion, ethics, music, theater, the arts, all mathematical and scientific knowledge, and the attitudes and values behind these. All these are memes. They evolve and thrive in a brutally competitive ecosystem. 
6. Social capital: the bonds which connect humans to each other to build trust, form families, tribes, towns, countries, and other hierarchies, and allow for cooperation and competition. 
7. Human capital: people and their abilities, which come from skills, insights, curiosity, effort, and talent. This is by far the most valuable form of capital, and we still massively underinvest in it. Energy, education, attention, creativity, and inspiration help form and constitute it. 
Most superorganisms like ants and bees tap out with just their species, social, and natural capital. What makes humans so prosperous is the intense level we have cultivated all these types of capital. We are generators of generators; we make capital.
The biggest challenge of the 21st century is how to grow the pie, that is, create as much capital on a Pareto optimal frontier – meaning figuring out how to grow all these forms of capital without making dumb tradeoffs (destroying the environment and natural capital in a bad way to make manufactured capital, for example, or destroying social capital for financial capital, or human capital for intellectual capital). The next biggest challenge is how to make sure all humans on the planet participate in this – that everyone becomes generators (not to keep redistributing the pie, per se, but enabling the bottom 1%, 10%, and 50% to increase their human capital and other forms of capital that come from that, like the social, intellectual, financial, etc). Small amounts of redistribution may be needed to get people basic Maslowian needs (food, housing, K-12 education, internet, etc), but ultimately the best way to grow the frontier is to empower everyone to be a capital generator.
 The “heads” in capital most likely referred to livestock, though in some societies it referred to “slaves” or “souls”. https://www.ahdictionary.com/word/search.html?q=capital
 PEP 255 is on Simple Generators in Python – a gem of an article. https://www.python.org/dev/peps/pep-0255/
 Douglas North on institutions: “Institutions are the humanly devised constraints that structure political, economic and social interaction. They consist of both informal constraints (sanctions, taboos, customs, traditions, and codes of conduct), and formal rules (constitutions, laws, property rights). Throughout history, institutions have been devised by human beings to create order and reduce uncertainty in exchange. Together with the standard constraints of economics they define the choice set and therefore determine transaction and production costs and hence the profitability and feasibility of engaging in economic activity… Institutions provide the incentive structure of an economy; as that structure evolves, it shapes the direction of economic change towards growth, stagnation, or decline.” https://ideas.repec.org/a/aea/jecper/v5y1991i1p97-112.html
 Pierre Bourdieu on cultural capital: “Cultural capital can exist in three forms: in the embodied state, i.e., in the form of long-lasting dispositions of the mind and body; in the objectified state, in the form of cultural goods (pictures, books, dictionaries, instruments, machines, etc.), which are the trace or realization of theories or critiques of these theories, problematics, etc.; and in the institutionalized state, a form of objectification which must be set apart because, as will be seen in the case of educational qualifications, it confers entirely original properties on the cultural capital which it is presumed to guarantee.” https://home.iitk.ac.in/~amman/soc748/bourdieu_forms_of_capital.pdf
 Ibid on social capital: “Social capital is the aggregate of the actual or potential resources which are linked to possession of a durable network of more or less institutionalized relationships of mutual acquaintance and recognition—or in other words, to membership in a group—which provides each of its members with the backing of the collectively owned capital, a “credential” which entitles them to credit, in the various senses of the word. These relationships may exist only in the practical state, in material and/or symbolic exchanges which help to maintain them. They may also be socially instituted and guaranteed by the application of a common name (the name of a family, a class, or a tribe or of a school, a party, etc.) and by a whole set of instituting acts designed simultaneously to form and inform those who undergo them; in this case, they are more or less really enacted and so maintained and reinforced, in exchanges. Being based on indissolubly material and symbolic exchanges, the establishment and maintenance of which presuppose reacknowledgment of proximity, they are also partially irreducible to objective relations of proximity in physical (geographical) space or even in economic and social space.
The volume of the social capital possessed by a given agent thus depends on the
size of the network of connections he can effectively mobilize and on the volume of
the capital (economic, cultural or symbolic) possessed in his own right by each of
those to whom he is connected. This means that, although it is relatively irreducible
to the economic and cultural capital possessed by a given agent, or even by the whole set of agents to whom he is connected, social capital is never completely independent of it because the exchanges instituting mutual acknowledgment presuppose the reacknowledgment of a minimum of objective homogeneity, and because it exerts a multiplier effect on the capital he possesses in his own right.”
 Gary Becker did the pioneering research on human capital: “Schooling, a computer training course, expenditures on medical care, and lectures on the virtues of punctuality and honesty are also capital. That is because they raise earnings, improve health, or add to a person’s good habits over much of his lifetime. Therefore, economists regard expenditures on education, training, medical care, and so on as investments in human capital. They are called human capital because people cannot be separated from their knowledge, skills, health, or values in the way they can be separated from their financial and physical assets.
Education, training, and health are the most important investments in human capital. Many studies have shown that high school and college education in the United States greatly raise a person’s income, even after netting out direct and indirect costs of schooling, and even after adjusting for the fact that people with more education tend to have higher IQs and better-educated, richer parents. Similar evidence covering many years is now available from more than a hundred countries with different cultures and economic systems. The earnings of more-educated people are almost always well above average, although the gains are generally larger in less-developed countries.” https://www.econlib.org/library/Enc/HumanCapital.html
Thanks to Pauline Prideaux, Madhan Gounder, and Ari Paul for reading drafts of this.