Functions and Characteristics of Money
Money solves a fundamental problem: how do you trade with someone who doesn't want what you have? Before money, people relied on barter, which was slow and limiting. Money streamlines exchange, gives us a way to measure value, and lets us save purchasing power for later.
The Three Functions of Money
Every introductory economics course comes back to these three functions. If something qualifies as "money," it needs to perform all three.
Medium of exchange means money is what people accept in trade for goods and services. Instead of swapping a chicken for a haircut, you pay with dollars. This eliminates the inefficiency of barter and dramatically reduces transaction costs (the time and effort spent making a trade happen).
Unit of account means money gives us a common yardstick for measuring value. Without it, you'd need to know the exchange rate between every possible pair of goods. With 100 goods in an economy, that's 4,950 different exchange rates. Money collapses all of that into just 100 prices. It also makes accounting and financial record-keeping possible, since everything is measured in the same units.
Store of value means money holds its purchasing power over time, so you can earn income today and spend it next month. This isn't perfect (inflation erodes purchasing power), but money is generally more convenient to store than, say, bushels of wheat. It also enables saving, lending, and borrowing, since financial contracts can be written in terms of money owed in the future.

Commodity Money vs. Fiat Money
These are the two major categories of money that economies have used throughout history.
Commodity money has intrinsic value. The material itself is worth something beyond its use as money. Gold and silver coins are classic examples. You could melt them down and use the metal for jewelry or industrial purposes. The downside: the money supply is limited by how much of the commodity exists, which can cause scarcity and restrict economic growth.
Fiat money has no intrinsic value. A dollar bill is just paper. It works as money because the government declares it legal tender and people trust the issuing authority. The advantage is flexibility: the central bank can adjust the money supply as economic conditions change. Virtually all modern economies use fiat money.

Money's Role in Replacing Barter
Barter requires a double coincidence of wants: both parties must want exactly what the other has, at the same time. If you're a farmer with wheat who needs shoes, you have to find a shoemaker who happens to want wheat. That's hard to arrange consistently.
Money eliminates this problem. You sell your wheat to anyone who wants it, receive money, and then buy shoes from anyone who sells them. The two transactions don't need to match up.
This has a deeper consequence: money enables specialization and division of labor. People can focus on what they're best at producing, confident they can trade money for everything else they need. Specialization is one of the main drivers of economic growth.
Economic Stability and Money
The value of money isn't fixed. When the money supply grows faster than the economy's output of goods and services, inflation results, meaning the general price level rises and each dollar buys less. When the price level falls, that's deflation, which can discourage spending (why buy today if things will be cheaper tomorrow?) and lead to economic slowdowns.
Central banks (like the Federal Reserve in the U.S.) manage the money supply and implement monetary policy to promote stable prices and healthy economic activity. How they do this is a major topic in the units ahead.