First things first, what is a participle?
Participles have a few different jobs. But, to make things easy, we’re only going to talk about their job as an adjective (modifier) which tells you more about the noun which follows.
Participles (in this job) often appear in the present tense, and often ends with “ing.” Speed is a verb, and speeding is its present participle. If you say, “Follow that speeding car,” the word speeding is telling you something about the car; and, is, therefore, a participle acting as an adjective.
Now, to understand how you dangle a participle, you need to understand participle phrases. They are phrases that contain a participle and modify the subject of the sentence. For example, “walking down the street, I noticed smoke pouring out of the building.” Walking down the street is a participle phrase which modifies the noun (subject) I.
When you dangle a participle, it means your participial phrase is hanging there in your sentence with no proper subject in sight. Like this: “Walking down the street, the bus stopped quickly.” Not only is this funny, (because as it is written, the bus is walking) it’s a dangling participle. The participle phrase, walking down the street does not tell us something about the only subject in the sentence (the bus). To fix it, we need to make sure that the participle has its appropriate noun. “Walking down the street, I saw the bus stop quickly.”