There are two basic types of gestures, co-speech gestures and emblems
Co-speech gestures facilitate the understanding of spoken language. They're not meant to be produced in the absence of speech. There are four main types:
Iconic gestures represent object attributes, spatial relationships, and actions. For example, think about how you would describe gesturally a tall person or a wide river as you were talking about each of those things.
2. deictic, or pointing
These gestures are pretty basic, connecting speech to another idea, object of location. For instance, if you were talking about someone across the room you might point them out to your interlocutor.
Metaphoric gestures put an abstract idea into a more literal, concrete form. Making your hands into a heart shape and placing them on your chest might indicate your affection for a loved one.
4. beat gestures
Basically, these just keep the rhythm of speech, and they convey no semantic content whatsoever. One example you may know is Bill Clinton's famous thumb wag:
On the flip side are emblems, which are capable of conveying meaning independent of speech. Some good examples are the thumbs up, the peace sign, and the middle finger. This Youtube video has many more, and illustrates how they vary by culture. I like this example very much, because just like words, so to do gestures vary by culture.