This is the 280th most frequent Czech word.
bývalý
"Former" or "ex-"
In this sentence, 'bývalý' signifies that the place used to be a hotel but is not anymore, highlighting a change in purpose or identity.
To bývalý hotel je nyní tělocvična.
That former hotel is now a gym.
Here, 'bývalé' (a form of 'bývalý') is used in plural to describe conversations that occurred in the past, indicating a prior time period relative to the present.
Pamatuji si na naše bývalé rozhovory.
I remember our past conversations.
Here, 'bývalý' is used as an adjective meaning 'former', describing a previous teacher the speaker had.