A segue is a smooth transition. When you segue in conversation, you change the topic so smoothly that people might not even notice.
A good speaker knows how to segue: they can get from one topic to another so easily that you hardly notice the topic changed. Comedians have the same skill as they segue from one joke to another, and politicians also learn the art of the segue. So do teachers. This is also a term in music for moving from one part of a piece to another. Remember that segue does not sound quite how it looks: it's pronounced "SEG-way."