How does a node forget about other nodes? It is said that addr message: Provide information on known nodes of the network. Non-advertised nodes should be forgotten after typically 3 hours.

I did not totally understood what does it mean forgetting a node? A node has a list of peers, and it is checking every 3 hours if these peer are active? Does it work like this? How does this forgetting mechanism work?
There is no need for a node to "forget" a node. This is not something that is required nor necessary. What Bitcoin Core does in response to a getaddr message (so it sends an addr message) is that it checks its list of nodes. It filters through that list for the things that it recently had a connection to and that it didn't have multiple failed connections to before. There is no checking that a node is actually live and it doesn't do it on a set timer either.