theObserver would like me to explain the difference between labor and labor power. So here you go.
According to the labor theory of value, economics in the broadest sense is the study of how human beings act on the natural, physical world to produce stuff we want. We define labor as an action that a) transforms the physical world and b) is instrumentally satisfying to the actor (the satisfaction gained by the product or outcome of the action, not the action itself, is the primary goal). Even picking an apple off a tree and eating it is labor: I am transforming the physical world by moving the apple away from its position on the tree to first my mouth, and then transforming it into mush by chewing it, and finally moving it to my stomach. Not only that, but I have to transform my own position towards the tree. The physical world is a given; the only thing human beings can do is choose how to act, how to allocate our labor.
In the narrower, modern, sense, economics is the study of how we labor specifically for the purpose of exchange, labor either directly performed for the benefit of someone other than the actor (services), or labor performed to create an object that will be given to someone else. Economists let the political scientists study slavery and psychologists study pure altruism; we study the processes by which people exchange their labor.
In real economics, we try to exclude the study of money. Either we abstract money away by dividing nominal values by price levels (e.g. we divide nominal GDP, total dollars exchanged, by price level in dollars; the dollars unit is cancelled) or we try to completely ignore money. Once we have excluded money, we are left with no unit to calculate costs except labor. So if we want to look at the real cost of a pair of shoes or a computer, we say it takes three hours of labor to produce a pair of shoes and sixty hours of labor to produce a computer. That's the total amount of labor, including, for example, the time it takes to make a shoe factory or all the factories necessary to make a computer, divided by the number of shoes or computers these factories will produce. The real absolute cost of something is the total amount of labor necessary to produce it.
There's a complication, of course: not all labor is exactly equivalent. Some labor is more-or-less intrinsically easier than other labor: an hour typing on a computer in an air-conditioned office is easier than an hour cleaning a hot, stinking sewer. Furthermore, not everyone is equally efficient: some people or companies can produce a shoe in only two and a half hours. Hence Marx introduced the concept of "socially necessary abstract labor time." This qualification becomes important down the road, but for our purposes now, we can make the simplifying (albeit unrealistic) assumption that all labor is exactly equivalent.
It is easy to see, then, that when we exchange commodities (goods and services), we are going to exchange them on the basis of equivalent absolute labor cost. If it takes sixty hours to produce a computer and three hours to produce a pair of shoes, then people will exchange one computer for twenty pairs of shoes. If Mike wants thirty pairs of shoes for his sixty-hour computer, then I'm just going to use sixty hours of my time to build my own computer instead of ninety hours of my time to make thirty pairs of shoes. In a more complex environment, I might not be able to produce a computer, but Alice will, and she will charge only twenty-five pairs of shoes to undercut Mike. Then Bob, Carol, Dave, etc. will get in on the action, each undercutting the other until the price has dropped to twenty pairs of shoes.
(There's also real relative cost, a.k.a. real opportunity cost, which is basically what we have to give up to get something else. An hour spent making shoes is an hour that cannot be spent making computers: we have to give up some computers to make shoes, and vice versa. But the real relative cost affects only the quantity of various commodities produced; it does not affect the real absolute cost, or that commodities are exchanged at equivalent real absolute cost.)
Workers are people, and people have to eat. They have to drink. They have to wear clothes. They have to live in houses. They have to rear children, who will become the next generation of workers. All these things have a cost. It requires a specific amount of labor labor to produce food, store clean water and transport it to people, create clothes, build houses, and educate children. The labor required to make all of these things comprise the total real absolute cost of living.
It seems clear that the total absolute cost of living per day in labor hours is substantially less than the number of hours a person can work in a day. If it were not, we would be living at a subsistence level. The difference between the cost of living and the total number of hours a person actually works in a day is the surplus value of labor.
In a capitalist economy, workers produce and exchange a particular commodity. But they are not producing and exchanging their labor directly as a commodity. They are, rather, producing and exchanging their ability to perform labor, what Marx labeled their labor power. There's a real difference between these two things. The cost of labor itself is the labor itself; labor is the cost. But the cost of labor power is the cost of living, which is substantially less than the number of hours of labor that cost of living makes available.
In a perfect market, the difference between labor and labor power wouldn't make much difference. The cost of labor power would simply act as a real floor on the quantity of labor produced: it could not be less than the number of workers times the absolute real cost of labor power. But there's no such thing as a perfect market: all the qualities* of a perfect market are unrealistic. Economists assume them to make the basic analysis more tractable, to isolate and describe, in some sense, the "essence" of one important force in economic behavior. It is one thing to make unrealistic assumptions to isolate some important force; it is quite another to assume that the ignored complications don't actually exists. And the essence of capitalism intentionally and systematically violates the assumptions of the perfect market.
*"Perfect market information, No participant with market power to set prices, No barriers to entry or exit, Equal access to production technology."
Capitalism, which is in essence the private ownership of the means of production, entails that there is privileged, unequal, access to production technology (the means of production) as well as barriers to entry in the capitalist class. There is a higher real cost, absolute and relative, for workers and their children to enter the capitalist class than for capitalists and their children to remain in the capitalist class. Furthermore, nominal (money) issues become important; capitalists have two substantial short-term monetary advantages. A capitalist will not die if his factory is shut down for a month; a worker will die if her income is absent for a month. Additionally, because there are many fewer capitalists than workers, capitalists have a much easier time colluding, and therefore becoming a cartel of price-setters. Thus when money is involved, the negotiations between capitalists and workers structurally and systematically push money wages down to the cost of labor power, rather than the absolute cost of labor.
Fundamentally, the question is this: how do capitalists make a profit? What does that profit really represent? Profit is, in nominal terms, the difference between the money collected from consumers (who are typically workers) and the money paid to the workers. We would have to get into monetary economics to find out where the extra money comes from (debt), but it real terms, what does that money represent? Money is demand, but what real thing does that money actually demand? In Marxian terms, the "extra" money represents a demand on the surplus value of labor, the labor performed by the worker that is not necessary for his survival and reproduction.
Also see The Labor Theory of Value