A present participle is a verb ending in -ing.
Running down the street, I fell over and bruised myself.
This sentence is made up of two clauses:
The main clause: I fell over and bruised myself.
The subordinate clause: Running down the street.
In this case, the sentence makes sense and can be understood easily. However, in the following example the subject of the main clause – me – does not come at the beginning of the clause but at the end:
Running down the street, my best friend nearly hit me.
Here it’s not possible to say who was doing the running: me, my best friend, or both of us.
Although the participle usually applies to the first item in the main clause (which is usually the subject) it does not have to so the sentence can read ambiguously.
So, when a participle is far away from the subject of the main clause we call it a Dangling Participle. Grammatically they are not wrong, however stylistically they can cause confusion and should be avoided.
The thief ran from the policeman, still holding the money in his hands.
Who has the money in their hands? The thief or the policeman?
I watched the old man peering through the window.
Who is peering through the window? Me or the old man?
Sometimes in the culture of ELT – English Language Teaching ironic reference is made to dangling participles or dangling modifiers to talk about pedantic and unnecessary concentration on grammar and the details of English at the expense of teaching or learning useful and functional English.
The issue of whether a participle is dangling or not isn’t really that important on the scale of TEFL in relation to, for example, verb tenses or SVO sentence structure. This means that in the school staff room when a teacher starts banging on about dangling participles they may not necessarily be speaking seriously!