A natural step from barter is a record of who owes what (so you don't have to bring some grain just to buy 1 beer from someone you have a good trust relationship with). A natural step from there is a token representing value, and there are lots of reasons to make them portable and interchangeable.

In very basic terms, it's a medium of exchange.

"Money" is not some objective, universal concept (although people think it is). It's not a naturally occuring phenomenon (I think I've read about chimps using some very simple mediums of exchange in the wild, which is pretty cool, but I think it's pretty exclusive to us and chimps). It's a human creation, and a tool to make our lives easier, much like any other form of technology.

It was created as a storage of some value you produced. Basically, by doing some work for someone, or giving something to someone, there was an exchange of value -- your item or your time/effort was worth something, and it was moved from your possession to theirs. If there was no money, you would need to immediately receive something else of similar value, or else the value would simply dissapear (you did some work and got some chickens, for example, which you could eat). Unfortunately, not all work is equal, and not all items of value are equal -- if you had 1 sheep, and your buddy had a cow, and cows are worth 2 sheep at that given moment, you could not do business. It gets even more complicated when services, rather than items, are provided. So we invented a system of "owing" value.

"Money" is not defined necessarily by currency, or by gold and silver, or anything else we've used throughout history. It can be anything, physically. In fact, it probably started out when, in small tribes where everyone knew each other, people simply kept track of favors and IOUs between friends and family -- and probably grew into physical items (like gold, or even seashells and tulips) [no citation, this is just my personal thoughts] once our communities expanded to the point where people were trading with strangers, or when it became to complex to trade mental IOUs (say I gave some guy 2 sheep, now he owes me 2 sheep's worth of stuff. The guy traded some other guy 2 sheep's worth of stuff. The third guy has a cow, owes the second guy 2 sheep/1 cow, and I want a cow. He can give me a cow and all debts between the three of us are cleared. However, even this simple example is pretty complicated). The point is, "money" is a concept, not a physical object -- the physical object, whatever it may be, is just a representation.

In fact, it basically boils down to debt. This is especially true in the current economic climate (where all fiat currency is basically backed by debt rather than any tangible item) but the concept of money itself is essentially "I did some service or provided some item of intrinsic value. I was provided with X amount of money for that service or item. Now someone owes me some service or item worth what I provided earlier." Another good analogy might be a ledger of value transactions (in fact, this would probably be the simplest form of money).

And so that's why we hear things like "the rich don't work for money, they work for assets." I remember that being a hard concept to wrap my mind around until I understood money as more than just what I buy stuff with. Money is a man-made creation, is not necessarily consumable, and has no intrinsic value beyond what society defines it to have (which can change at a whim). But if you own something with intrinsic value (can be consumed or produces something that can be consumed -- like a business/product, land, etc.) you can continue to produce value that can be exchanged for whatever passes as "money."

I hope this makes sense. I think the hardest part of explaining it (and why you probably can't find a definite answer) is because it's an abstract concept.