What are participles?

A participle is yet another verbal, a word derived from a verb. Participles are verbals that act as adjectives.
That dripping faucet kept me awake all night.
Dried meat and preserved fruit were staples for our ancestors.
This movie is boring.
A broken clock stood on the mantelpiece.

Participles can look like present participles (base form of verb + -ing) or like past participles (base form + -ed for regular verbs, or the various irregular past participles). Participles in present form usually describe what a thing does. Participles in past form usually describe what was done to a thing.

Do not confuse adjective participles with participles that are part of verbs.

She is buying a talking bird for her daughter.

Is buying is the verb buy in present progressive tense. Talking is a participle modifying the noun bird.

Participles frequently occur in participial phrases.

The woman sitting in front of me was so tall I could not see the stage.
Knowing you would disapprove, I could not lie to him.
Calling the horse's name, she ran through the snowstorm.

When a participial phrase comes at the beginning of the sentence, it should modify the subject of the sentence. If it does not, it is called a dangling participle. (Watch out for these! Dangling participles are a favorite blunder for teachers to highlight in your essays.)

Dangling participle, incorrect: Walking through the forest, the trees were beautiful.
It sounds like the beautiful trees were walking!
Correct: Walking through the forest, we saw many beautiful trees.
We saw the trees while we were walking.