My gums are loose between my teeth. is this normal?

Not normal: You may have periodontal problems. See a dentist at once for evaluation and possible treatment of the problem.

No: You may have very inflamed gums due to active gum disease. See a dentist for a definitive diagnosis.

Not really: You could have a form of periodontal disease. The bacteria that has progressed under your gums, causes a loss of attachment from the teeth and usually "pockets" form that the dentist will evaluate. And in some, they will notice that the gums feel "loose.".