To sit tight is a strange English idiom and it literally means that you sit down squeezing your body in a tight way, which if you did it would be very uncomfortable, not to mention you’ll look really strange.
But if a person tells you to sit tight they want you to wait patiently and take no action until you hear otherwise.
“Mrs. Carter, do you have any idea when the exam results are going to come out?”
“Who knows Johnny, sometimes they come out quickly but it could take some time. You’re just going to have to sit tight and wait.”