Because face it, it's not nice approaching an audience that you don't really know (though you should try and get to know them beforehand) and having your brain lie to you that no-one really likes you and that everyone can't wait for you to fail...
Now 99% of the times when you'll be engaged in public speaking that probably won't be true. The audience wants you to succeed, but to help convince yourself that this is true, I recommend you use humor.
Power of Speech Humor - They Laugh... and You Relax
When you can share a joke or a funny quote or anything that will get people chuckling, you've had your ice-breaker and the room (and the audience) will seem miles less threatening.
Speech Humor thus has a confidence building effect on you, the speaker, and a relaxing effect on the audience. This win-win tool is often neglected by serious speakers who feel that "funny-stuff" simply do not belong in their speeches.
A language teacher in high-school once told me that humor is almost always fitting, even at a funeral. I have tested his advice, and found it to be true: In most cases, humor will not detract from the meaning of your message or its seriousness. It might even bring the audience to a place where they can better understand your message.
So use wit and speech humor to your advantage: Look up specific jokes related to your topic and weave them into your speech at different intervals. Also, don't be scared to tell funny stories from your own life. Audiences love authenticity.
Anyone who's ever been to a business-retreat, a boy scouts meeting, or a youth-camp will know what I'm about to describe:
I used to hate these when I was still in my schooling years, but to my dismay I've found that they're often used in the adult world as well. Especially when the people in charge want to enforce social contact between unwilling participants (like me).
They either take the form of a silly game where you have to meet and speak to people that you would normally avoid, or an activity of sorts that will start of uncomfortably, but end up with you getting to know new people.
And they're called "ice-breakers" for a reason. They're cryostasis for the mind. They unfreeze everyone to the point where the social temperature in the room becomes acceptable and everyone settles into a comfortable oh-yeah-I-know-this-guy-and-that-guy and I'm not such a stranger anymore...
Well speech humor is an excellent ice-breaker. And one that smart public speakers utilize to their advantage. Because nothing will as quickly and effortlessly change the perceived atmosphere in the room from being cold, formal and stiff, to one of relaxed openness, as a poignant joke, a witty saying or a laugh-out-loud quote will do.
Humor has been a personal favorite of mine and a tool in my public speaking arsenal that gets pulled out pretty early on in my speeches. In fact, I usually try to open my speech, where appropriate with a joke or a funny remark.