To stammer — or to have a stammer — is to speak haltingly and to have trouble getting the words out. A stammer is also called a "stutter."
Stammering (or stuttering) has a couple of related meanings. A stammer is a serious problem for some people who have great difficulty speaking. They have trouble getting the words out, and their language does not flow. They might get stuck repeating one sound over and over again. This is a difficult problem to overcome. However, we all stammer sometimes, often because we're confused, scared, tired, or unsure of what to say.