Hard fork or soft fork: what happens to your coins in a split?

A fork is a change to the rules by which the computers of a blockchain network reach agreement. The practical question behind it is this: do you get new coins out of it, or not? The answer hangs on a single difference. In a hard fork, a blockchain can split in two, with both running on separately afterwards, and you then hold the same number of coins on each side. In a soft fork, one blockchain remains, and nothing new appears in your wallet.