Understanding capitalism requires understanding a constellation of concepts that reinforce each other. I'll try to make some headway here.
A helpful way to think about capital is as the aggregate of all non-labour inputs to production. Some would include land as a factor of production as well, and some others would consider human capital to be a form of capital (typically when explaining why capital in aggregate does not run up against the problem of diminishing marginal returns.)
The defining characteristic of capitalism is that capital is privately owned. As you can see, it is compatible with a great diversity of political systems (ranging from the illiberal democracies of Singapore, to the authoritarianism of China, to the democracies in the West). Because capital is privately owned, it is typically invested in such a way as to maximise profit. This isn't necessarily the case, and some people might invest their private wealth in non-profit organisations. But the dominant paradigm is typically acquisition for private gain.
The term became popular in its modern usage sometime in the middle of the 19th century, possibly slightly earlier. Marx was probably not the originator, but he was definitely contemporaneous with others who did. Potentially Proudhon and socialists of other stripes. Since then the left has kept this usage alive, together with the oft-mentioned 'bourgeois mode of production' - which is essentially synonymous.
The capitalist is likely to speak of capitalism being conducive to human freedom (freedom to buy and sell, enter into contracts), and to the generation of wealth and prosperity for mankind. He is likely to speak of its efficiency with respect to classical economics - the invisible hand through the price mechanism equilibrates supply and demand, so that the market clears (everyone is satisfied). And possibly, that capitalism encourages thrift and industry - which are virtues (although, this is susceptible to the immediate retort that we are conditioned to think of these as virtues, because they are useful within capitalism, not because they have any timeless worth).
Anti-capitalisms (two main types, with many sub-types)
1. A Normative Critique
The main line here is that capitalism is unjust and causes us to detract from the good life. There is substantial trove of academic debate on whether Marx himself thought capitalism was unjust. (c.f. Norman Geras, "The Controversy about Marx and Justice).
The most common type of this critique is - capitalism leads to inequality in resources. Some people may regard this as intrinsically negative, which is up for debate. But this inequality typically translates into unequal political influence - which we see in the form of corporate lobbyists and other distortions to the democratic process.
Some other normative critiques (nowhere near exhaustive):
Capitalism is exploitative - maximising profit involves underpaying workers and denying them the fair share of the revenues.
Capitalism is coercive - while people may seem to voluntarily enter into labour contracts, the reality is that they have very little other option. Back in the day when peasants had some land - they could get by on subsistence farming. The modern-day proletarian has no such option. Notice that it is not an issue of whether the proletarian (working-class man) is better off or not, it is an issue of whether he is free to choose or not.
Capitalism is alienating - it prevents us from working in the right sort of way, that which actualises our potential. We are stuck doing pointless jobs - like waiting fast food tables, when simple etiquette would do without it, or shuffling papers within an engorged bureaucracy, telemarketing, or roadsweeping, when machines can do it so much better. Because what maximises profit doesn't necessarily coincide with what develops our potential, there is a problem. Capitalism also alienates us from our fellow man - we see each other as potential consumers, or labour, which prevents us from relating in a dignity-preserving way.
2. An Efficiency Critique
Capitalism is inefficient, and squanders our natural resources. In the Marxian lingo you would hear about capitalism being 'a fetter on the productive forces' at some point in future (1859 Preface to a Critique of Political Economy). The idea is that the productive forces (labour, machinery, natural resources...) have a tendency to develop, and the relations of production we choose have a bearing on how effectively the productive forces can develop. Capitalism has unleashed great productivity, but those who subscribe to a Marxian view of history are pessimistic about whether it will always be conducive to the development of the productive forces.
From the Greens (environmentalists) you might hear about how capitalism takes a myopic view and systematically disregards environmental externalities. When selfish interests dominate government policy-making on the environment, there is wanton environmental degradation in the service of profit. This is often brought across in ethical terms - but considerations of natural resource scarcity lead me to consider it an efficiency-based critique, at least in part.
Hope this helps!