Cheered to the rafters

"Mr X was cheered to the rafters when he (did something very well)..."

I have searched this sentence in Google but I was only able to "catch" its general meaning (at least, I suppose it's used for people to express a great appreciation to artists or politicians, for example when a singer's performance has been excellent and people clap their hands for a very long time)
So, What does it exactly mean?
How shoud I read the word "rafter(s)" here? (any of the parallel beams that support a roof / one who maneuvers logs into position and binds them into rafts / one who travels by raft) see this page
I'll greatly appreciate your help about the above!

Thank you!