This idiom or expression has to do with:

Training someone, as in:
It’ll take a few days to break in our new secretary.

The initial period of usage, as in:
I’m not supposed to drive my new car too fast during the recommended “break in” period, which is the first 3000 miles.

Entering a place without permission or authorization, as in:
There was a break in at our company headquarters earlier today.

Also see:
Breaking into a place.