I think it talks about closing a channel?

Based on what I understand the timelock expires is I think the dispute period according to the wiki if you didn't find the protocol breach all the funds that you received from your open channel will be gone but the deposit amount when you open a channel you can still able to take them out with fees.

protocol breach looks like you need proof that your partner is a cheater or doing fraud most cheaters or fraudsters send/broadcast outdated data with the incorrect distribution. So to avoid it you need to broadcast the most up-to-date settlement transaction to the network.

I think wiki explains better that the link you shared above read this https://en.wikipedia.org/wiki/Lightning_Network