Handwaving over a lot of the complexities, human effort over time creates items of value by transforming physical reality. The transformation can be as simple as finding a piece of fruit on a tree and moving it to one's mouth, or as complicated as turning silicon, copper, gold, etc. into a supercomputer. Labor is human effort over time that actually creates value.
We have found, over history, that we can use labor to produce "stuff" (not just physical stuff, but also services, ideas and technology) that makes subsequent labor more efficient, i.e. we can create more value with less human time and effort. We have to incur the costs (use the labor) to make this stuff before we actually make stuff that has intrinsic value. We can label as capital anything we have to use labor for before we begin producing stuff we just consume (i.e. stuff that has intrinsic value); the stuff we create to make later production more efficient is physical and intellectual capital.
Furthermore, if we accumulate or can generate a sufficient surplus, we can feed a lot of people for a long time so they can create complicated stuff with intrinsic value (such as computers, airplanes, moon rockets, etc.). Since we have to incur the cost (use the labor to feed the people) well before they produce the value, this cost is essentially a capital cost; it is human capital.
(I'm presently ignoring the further criteria having to do with the exchange of stuff. These criteria will become important later.)
Capital makes our labor more efficient. It does so directly by allowing us to produce more value with less labor time. It also does so indirectly by allowing us to take a long time to produce high value stuff; we could produce only lower-value stuff if we couldn't work for a long time before creating something.
The actual labor necessary to produce capital must be paid for. But, generally speaking, capital "pays for itself" very quickly: the increased value afforded by the use of capital exceeds its labor cost by orders of magnitude. Even late in the 18th century, Adam Smith observed a two to three order of magnitude increase in efficiency in the manufacture of pins. [Wealth of Nations, 1776, Chapter 1, section 1.1.3] (The primary proximate cause of this increase of efficiency was division of labor afforded by the accumulation of capital. The division of labor by itself poses interesting questions at all level of political-economic analysis, especially in game theory.)
Once the actual labor involved in creating the capital has been paid for (however we happen to construe "paid for") what do we do with the additional value the capital affords through increased efficiency?
Under capitalism, private individuals own this additional value, and they may consume or invest it as they themselves please, for their own and no others' benefit. In theory, just as the benefits to the subjects were supposed to emerge from the interplay of competing private benefits of the royalty and nobility, the benefits to the workers are supposed to emerge from the interplay of competing private benefits of the owners of capital. The communist argument says that it is a matter of scientific truth established by empirical observation that benefits to the workers do not actually emerge from the interplay of private ownership of capital*, therefore we must directly socialize the ownership of capital.
*Technically, some minimal benefit to workers does emerge from the private ownership of capital, but not nearly enough.
Of course, I will be elaborating on this argument in considerably greater detail in future posts.