Could a short circuit in your breaker box turn a bunch of lights on in your house/?

Why not provide a more in-depth description of what happened? Is this residential?
Are there any contactors?

My daughter and boyfriend were standing in their kitchen at 9:30 at night (residential house) they heard a large thud/boom sounded like somewhere in the house that shook the floor a little bit. They walked around the outside and looked all through the house and found nothing out of order. HOWEVER; the basement lights were all on and they weren't before. Even a light that didn't turn on previously. They only lived there less than a week. Of course my daughter is totally freaked out now. BTW the basement is all finished. Direct TV installer was there the day before if that matters at all. Thanks...

This smells like a coincidental occurrence... Loose wires that are jarred into making connection from a switch or circuit breaker might explain this.
Do you own this or rent? Either way you might hire an electrician to see if the switches and receptacles are "back wired" which may be the intermittent contact issue and to check and identify any other issues... it may help your daughter sleep better.