I'm not sure whether the OP was referring to an instrumental break in the middle of a song, or just the short instrumental 'fills' between verses that you often get, for example playing the last couple of bars of the tune again before going into the next verse.

I sometimes do play (ability permitting) an instrumental break in the middle of a song to hopefully add a bit of variety for the listener, and possibly give my voice a break at the same time. I think some songs benefit from the short fills in between verses, as it allows the audience time to think about what's been sung. For example, if it's a humorous song, the 'fill' allows for laughter, which would otherwise drown out the first few words of the next verse.