I have always wonder why dose The Tonight Show with Jay Leno and The Late Show with David Leterman run fr4om 10:35 pm until 11:37 pm

The idea was to give the local stations an extra 5 minutes for the late news, that both shows usually follow.

but I am wondering how come the run 2 mintues over

I suppose that has to do with you and your local TV station's clocks being slightly off-synchro

what does off Synchro mean

No, almost every night Leno runs until 12:37 ET time. Never knew why.

where I live we do not get The Late Late Show until 12:10 am Central Time

what does off Synchro mean
it means your clock and your local stations clock probably don't have the same time.