Good transitions can make a speech more important to the audience because they feel they are being taken to a positive conclusion without having to travel a bumpy road.
It's true. The smoother the road you lead your listeners along, the more willing they are to follow. Transitions make the road smoother because they are one of the three aspects to organization. The first two are outlining and sequencing (putting the ideas in the order in which you will present your information). But transitions are also important for several reasons. They are logical extensions of the thoughts that came before; they help you get from one idea to the next. They also act as signposts to tell your audience that a new idea is coming.
Imagine that you are driving through the state of Florida, and you want to visit Key West, America's southernmost city. There's one problem. Key West is located at the end of a series of islands. Once you reach the tip of the Florida mainland, you're sunk—or you would be, if it wasn't for the bridges. Each Key is linked to the next by a succession of overseas bridges that make it possible to travel easily from one island to the next (and the next and the next) until you reach your destination.
Presentations are like the Florida Keys in that they're made up of a series of separate ideas that have to be linked together. The only way to get from one to another is by building linguistic bridges; those bridges are what we call transitions.
Speakers tell me that transitions present some of the biggest problems they have in their presentations. Many speakers concentrate all their ammunition on the opening, thinking that with a strong start, the rest can just follow. Not true. While an attention-getting opening is crucial to the beginning of a detail, the challenge is to keep the ideas that follow just as vivid.