Let's say you have 2 key pairs as part of your identity. You sign a message with key 2 and publish it on the blockchain at block height H. Then at some point in the future, you lose the private part of key 2 or it becomes compromised. So now you sign a message with key 1 that says "replace key 2 with key 3 from this point on" and you publish it to the blockchain.

Now, any messages signed with key 2 before the replacement can still be deemed valid, but any future messages signed with the compromised key will not be valid.