A modifier is a word or phrase that describes or explains another word in the sentence.
I only went to school on Friday.
In this sentence, the word "only" is a modifier. Right now, it modifies the word "went" because it is closest to that word. The sentence could mean that on Friday the writer did nothing else but go to school. But suppose the writer wants us to know that last week she went to school only on one day. In that case, the sentence should read
I went to school only on Friday.
You need to be careful about where you place modifiers because a misplaced modifier can cause grammatical problems.
Example: The Skidmore student was told that she had been expelled from school by the professor.
Was the Skidmore student told by the professor that she had been expelled? Or was she told by someone else that the professor had expelled her? Who expelled her and who told her the news? Are they the same person? The sentence ends up being too confusing.
Here is the same sentence revised:
The professor told the Skidmore student that she had been expelled from school.
Now it's clear that the professor is the person who told the Skidmore student the unfortunate news.
Having completed the assignment, the television was turned on.
The problem here is that this sentence says the television completed the assignment. We can guess, since televisions don't generally do that sort of thing, that the person who turned on the television is missing from the sentence. We can revise the sentence by adding a subject for the first part of the sentence to modify:
Having completed the assignment, Jonas turned on the television.
Notice that the introductory phrase "having completed the assignment" refers to Jonas.