I think the answer you're probably looking for is the exact same reason why capitalism is one of the most functional (even if not "the best" and certainly not the most equitable) economic systems come up with so far: people are greedy.
In general, people aren't willing to do something for nothing. Some people exhibit this more openly than others. For example, some people who are "really greedy" are unwilling to do even the most basic of humanitarian tasks, such as holding a door for a pregnant women, without some form of compensation which they may overtly even ask for. Others are more subtle: they may be willing to do "favors", especially for "friends" on the sole grounds of "tit for tat". Basically, they expect to be repaid with a similar degree of thought or useful activity at some later, perhaps undefined time.
And hence we have arrived at a barter economy. You may need some widget designed. I happen to design widgets. I'm willing to design a widget for you, but I expect something in return. If I know you, trust you, am friends with you, etc., I may be willing to do things informally e.g. I'll design your widget now, and, some time in the future, maybe you'll help me repaint my house or bring some food home for me. However, if I don't know you well, I'll probably want to have at least the terms up front, and I'll probably want things resolved in short order e.g. I'll design your widget now and in return you agree to paint my house in full the weekend after I complete the design and deliver it.
Ah, but we have a problem. Suppose you are really only good at painting houses (you may be REALLY good at it - it's your specialty - but you're not good at much else), but my house was just painted last month. It probably doesn't need painted again. Likewise, I'm the best widget designer in town. You'd be a fool to have somebody design you a widget based solely on their need for having their house painted. You have a couple choices: you can either work out some convoluted, multi-party trade, or everybody can generally agree on some neutral arbiter of "favors owed". That neutral arbiter is money.
And hence we arrive at a capitalist/market driven economy. You can efficiently trade goods and services using this neutral representation of value and wealth that is money. Your employer will happily accept service from you ("work") and give you money. That's fine by you because your only other option would be to have him give you the product of your services right back (since that's all he has, absent other trades), and that's probably not very useful to you. You can take your money and give it to someone else in exchange for whatever the two of you agree on. You've removed the need to involve everybody in a single transaction just to trade arbitrary goods and services.
Of course, if nobody was greedy, this wouldn't be needed. We could do everything on the informal basis. The problem is that if you're informal, sometimes you'll get screwed over. I might design that widget, and you might use/sell them to people in exchange for services/goods they can provide, but you may welch on your obligation to me indefinitely. If you're really a friend, I probably don't care a lot, because I value our friendship for other reasons, but if you're just some Joe, I'm probably pretty miffed that you didn't do anything in return. And chances are, if you're greedy, you'll welch on any obligation you can. But if we have money, I get paid at the end, and that's that.