Two kinds of fork
A fork is a change to the rules. The difference between the two kinds is what happens to the computers that don’t upgrade.
A soft fork tightens the rules. Blocks valid under the new rules are also valid under the old ones, so an old node keeps following the chain even though it doesn’t understand everything in it, as long as most of the mining power enforces the new rules. Most of Bitcoin’s upgrades have been soft forks for this reason: a node that doesn’t upgrade stays on the network.
A hard fork loosens or changes the rules so that new blocks are invalid to old nodes. Everyone has to upgrade, or the network splits into two chains that share a history up to the fork block and disagree ever after. Ethereum upgrades this way, with the whole network moving together; Ethereum Unlocked 1 lists the upgrades.
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