Why is it important to speak clearly?

Answer:

So that people can understand what you say, and that's the whole point of speaking in the first place.
The way you speak is also a clear indication on how much confidence you have in what you are saying and how much you believe in it. People who mumble or don't speak clearly are less likely to be seen as honest or confident. If someone were to answer a question completely and intelligently, but mumble at the same time no one would give that response the time of day.
Mumbling also shows you have no confidence in what you are saying so why would anyone else. It's the same as shrugging your shoulders at someone when they ask you a question.