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There are a lot of parts to inflation, but I'll do my best.
Money is used as a medium of exchange. It's convenient, easily countable, and an agreed upon unit of value. A dollar is a very, very small slice of the entire worth of the economy. As processes improve and production increases, the economy gets bigger. Because of this, we need more dollars to divide it into smaller pieces. The Federal Bank "prints" money to give us smaller pieces of the economy we can use. That's why we have "more" money. Your wealth is the same; it's just represented using more dollars. This is the Money Supply.
When you say inflation, and you're referring to the pinch you feel in your wallet, generally that's when the money supply grows faster than the economy is growing. For example, after WW1 Germany began increasing the money supply to repay loans for postwar reparations. But without the economy floundering and the money supply rapidly growing, they experienced intense inflation. The money people had was becoming a smaller slice of the same economy. It was becoming worth less.
Inflation is rather complicated. I had a whole semester about it in college, but generally, this is what it is.