A participle is a word made from a verb but used as an adjective.
The students approached the abandoned house nervously.
A participial phrase contains a participle and words that modify it.
Entering the house, they heard a spooky noise.
A participle or a participial phrase should appear close to the word it modifies. A dangling participle is an error that occurs when it is not clear which word the participle modifies.
Consider the following sentence:
We saw an owl driving through the woods.
Unless that owl was actually driving a car, the sentence must be corrected, because it contains a dangling participle. Probably, it is supposed to read:
Driving through the woods, we saw an owl.