A dangling modifier does not seem to modify anything in a sentence. It dangles, unconnected to the word or words it is intended to modify. Frequently, it produces funny results:
     When still a girl, my father joined the army.
     It sounds like "father" was once a girl! The problem is that the person to which "When still a girl" refers (in this case "I") is missing. Here's how to correct it:
     When I was still a girl, my father joined the army.
     Dangling modifiers usually occur at the head of a sentence in the form of an adjectival clause, with a subject that is implied but never stated.
     After lifting the heavy piano up the stairs, the apartment door was too small to get through.
     Did the apartment door lift the heavy piano up the stairs--?! Really? Wow! I wish my apartment door could do useful things like that! Here's a correction:
     After lifting the heavy piano up the stairs, we discovered the apartment door was too small to get it through.
     My personal favorite? Oh, man.... I've seen so many wacked out and wiggy dangling modifiers! Am I jaded, boys and girls? You know it!
     Running to the car, my keys fell to the pavement.
     Can you make the correction? We know keys can't run to the car, right? Even in a galaxy far, far away that's not likely to happen. Here you go:
     Running to the car, I dropped my keys on the pavement.
     In all seriousness, now, the fact is simply this: dangling modifiers in your writing are evidence of your not knowing how to use your instrument, in this case language, properly. Bush league stuff, babe. Strictly unprofessional! It's like a musician playing with a symphony orchestra and hitting wrong notes. How long do you think any symphony orchestra is going to keep a musician who plays wrong notes? This isn't a three-strikes-yer-out proposition!
     You can quickly professionalize [at least this aspect of] your writing by taking this small lesson, respectfully submitted here on this page for your edification.