1) Transitions. 2) Significant moments (like a poignant story or really powerful statistic) 3) Your credibility as a speaker (i.e. being confident) 4) The tone of the speech
You'll want to identify these points in your speech first, then decide how to use non-verbal communication to get them across. Here are few ways you can do this:
Gestures: As Karen and Kimberley both said, using gestures sparingly and effectively can be helpful. For instance, using gestures, such as pointing with your whole hand, palm out (not pointing with fingers - that can be seen as rude) to indicate items in a list makes it easier for the listener to follow you. Don't just throw your hands around. Make sure your gestures look deliberate.
Movement: I would also suggest not giving a speech behind a podium as we tend to lean on things. Instead, I'd strongly suggest using movement to guide your big transitions. If you move from one point in your speech to another, you can walk across the space to keep the listener interested and to help them SEE the transition. You can walk shorter lengths, or even take a step or two, to indicate smaller transitions.
Eye contact and posture: When speaking in public, you want to appear confident. Look people in the eye, scanning the room. Don't stare too long at one person. You should also pay attention to your posture. Holding your shoulders and face up will engage people and make them want to listen to you.
Pause: Kimberley and Karen pointed out the importance of pausing. Pausing at moments where you want the listener to think helps them process the words you are saying and can establish a tone for your speech. Speaking too fast makes your speech seem less serious, or maybe way too serious, like everyone needs to get out right away. Don't be afraid of silence. It can be really powerful.
Be put-together: Although you don't need to extensive lengths, if you're speaking in public, you will want to look presentable. Even a business casual outfit and combed hair can do the trick. This all goes back to looking confident. You want people to take you seriously.
Remember to keep everything in moderation. You wouldn't want to watch someone running back and forth across the stage constantly, but you also don't want to watch someone who doesn't ever move while they talk, right?
