What does it mean if my baby has trouble swallowing?

Depends. Swallowing problems can be from many causes and should be addressed with the help of your pediatrician and maybe a feeding expert (such as an occupational therapist) or an ent. Less serious causes (sore throat) resolve quickly. More serious causes include a mass in the throat, developmental delays, severe reflux, anaphylaxis, and more. These should all be discussed with your baby's physician.
Needs visit with MD. I would want more information on what exactly is going on. I would suggest a visit with your pediatrician. The first thing that comes to mind based just on the question is does this child maybe have some mouth/jaw weakness that would benefit from an oral motor evaluation. The best answer is one obtained in a face to face visit with your physician.