In grammar, a dangling participle is an adjective that is unintentionally modifying the wrong noun in a sentence. An example is: "Walking through the kitchen, the smoke alarm was going off." This sentence literally means that the smoke alarm was taking a stroll.
It's not hard to use a dangling participle inadvertently, but these pesky participles are easy to fix. When you say, "Speeding down the hallway, the door to his math class came into view," speeding is the participle (an adjective formed from the -ing form of a verb). Because it's dangling, unconnected to the person who's speeding, it sounds like it's the door that's speeding down the hallway. Instead, say, "Speeding down the hallway, he saw the door come into view."