An onomatopoeia is a word that imitates a sound.  The easiest way to understand onomatopoeic words is by giving some examples.
Animal noises are a great place to start. Think about the words that are used to describe the noises that animals make. Words like moo, oink, chirp, meow, woof and roar all sound like the noise that comes from the animal themselves.
Water also often has onomatopoeic words associated with it. For instance, the word drip sounds like the noise that is made by dripping water. Likewise, plop, splash and bloop all imitate the sounds that water makes.
Words that describe collisions or objects bumping into one another also are often onomatopoeic. Some great examples include bang, thud, boom, thump, clatter or clank. 
You can even look at cars, boats and trains for examples. Words like vroom, chug, honk, screech, beep-beep and choo-choo all describe the sounds that these modes of transportation make.
These fight scenes from the class Batman series provide some more great examples of onomatopoeia in action: