A 'dangling participle' means that the participle in an opening phrase doesn't relate to the sentence's main subject. It's easier to see from examples:
- Sulking in his tent, the battle commenced without Achilles.
- Not being in favour of military conquest, peace and prosperity were Augustus's preferred strategies.
- After drinking the poison, death came quickly to Socrates.
In the first example, the participle is 'sulking' and the main subject is 'the battle'. Written in the example form, the sentence implies that the battle is a man and was sulking.
In the second example, the participle is 'being' and the main subjects are 'peace and prosperity'. Written in the example form, the sentence implies that peace and prosperity are living things, and not in favour of military conquest.
In the third example, the participle is 'drinking' and the main subject is 'death'. Written in the example form, it seems that death drank the poison.
It's not enough to say 'well, the reader will know what I mean'. Learning to write clearly is all part of your university training, and avoiding dangling (also called 'unrelated') participles is part of that process.
Fixing dangling participles is not hard. Just make sure the subject is directly related to its verb.
- As Achilles was sulking in his tent, the battle commenced. (Achilles/sulking; battle/commenced)
- Not being in favour of military conquest, Augustus preferred peace and prosperity as strageties. (Augustus/preferred)
- After Socrates had drunk the poison, death came quickly. (Socrates/had drunk; death/came)