When a new commitment transaction is made, the old one should become invalid. However commitment transactions are not broadcast to the network, rather they are kept private and only broadcast when you want the channel to close. But because all commitment transactions are technically valid, we need some way to prevent people from broadcasting old commitments as they would effectively allow them to steal money. That's where the revocation key comes in.

During the process to create a new commitment, the revocation key for the commitment being invalidated is revealed to the other party. In this way, if you were to broadcast the old commitment, the other party would have the revocation key and can thus broadcast a punishment transaction where they use the revocation key to take all of the funds in the channel.

The revocation key itself is basically the combination of two keys. What effectively happens is that both parties provide a public key at commitment transaction creation time, and those public keys are combined to create the revocation public key. Then when the commitment is replaced with a new one, the party who is having their commitment revoked (remember that each party has their own personalized commitment transaction and the revocation keys are "personalized" for each commitment) reveals their revocation secret to the other party. This secret is combined with the other party's own revocation secret to create the full revocation key. In this way, the party who would have his commitment revoked with that key does not have access to the full revocation key.