As we all know, if you flip a coin that has an equal chance of landing heads as it does tails, then if you flip the coin many times, half the time you will get heads and half the time you will get tails.

When discussing this with a friend, they said that if you were to flip the coin 1000 times, and lets say the first 100 times it landed heads, then the chances of landing a tail was increased (the logic being that if it is unbiased, then by the time you have flipped it 1000 times you will have roughly 500 heads and 500 tails, so tails must be more likely).

I know that to be a fallacy, as past results don't influence future results. Is there a name for that particular fallacy? Also, is there a better explanation of why this is fallacious?

It's called the Gambler's fallacy.