I thought of writing this article on modifiers, which seem to confuse a lot of folks over here. This is a slightly advanced concept (and read this only if you have a good understanding of verb-ing, verb-ed and noun modifiers.

What is a modifier
A modifier is a word or a phrase or a clause, that modifies an entity in a given sentence. Usually, a modifier can be removed without altering the meaning of the original sentence, because a modifier gives additional information about the entity, it describes.

Let's discuss an example.

Ex: Amidst the ashen colored grass, I saw a fully grown beast with an alternating brown and white coat and a distinctive black streak across its back, accounting for its visibility from a quarter mile.

Construction: Prepositional phrase + subject + modifier + main verb + object + Prepositional phrases + modifier

Removing all the prep. phrases and modifiers, we have, 'I saw a beast' as the original sentence

If you remove a modifier, the meaning of the sentence won't change.



Examples of each type (limiting only to phrases and clauses)

Absolute phrase
1. Its surface temperatures estimated at minus 230 degrees Fahrenheit, Jupiter's moon Europa has long been considered far too cold to support life.
The absolute phrase is modifying the main clause that follows.

Since the absolute phrase modifies the entire clause, it can be placed either before or after the main clause.

Participle phrase
2. Local shrimpers held a news conference, saying that their compliance with laws requiring turtle-excluder devices on shrimp nets is protecting adult sea turtles

comma + saying is modifying the preceding clause.
requiring is a verb-ing modifier (present participle modifier), modifying the preceding noun - laws

comma + ing modifier will present additional information about the preceding clause by associating itself with the subject-verb of the preceding clause.

3. The increased popularity and availability of televisions has led to the decline of regional dialects, language variations originating from diverse ethnic and cultural heritages and perpetuated by geographic isolation.

originating is modifying the preceding noun - language variations
perpetuated is a verb-ed modifier (past participle modifier), modifying the preceding noun - language variations

Not all -ing ending verbs are present participles. There are something called gerunds too.
a. Walking on the beach, I stepped on a broken piece of glass.
b. Walking on the beach is dangerous if glass pieces are lying around.

a. is an example of participle phrase. It is modifying the pronoun 'I'.
b. is an example of a gerund phrase. It is the subject of the verb 'is'.

Prepositional phrase
4. Until almost 1900, scholars and critics did not begin seriously to study traditional Native American poetry.
The prepositional phrase is acting as an adverb, answering when.

5. The book on the table is covered in dust.
The prepositional phrase is acting as an adjective answering which one.

A prepositional phrase will never contain the subject of a sentence.
Consequence of this is far fletched as you can see in the below examples.

a. Neither of us is present.
The verb is is singular and so is aptly in agreement with the singular form 'is'

b. The TV, along with the radio, has become an integral part of our parents.
The verb has is singular and so is aptly in agreement with singular form 'has'

Adjective clause
6. a. The mouse, which is grey, is about to eat the cheese on the mousetrap.
The adjective clause is a relative pronoun clause and introduces non-restrictive information.

b. The mouse that was killed in the mousetrap is grey.
The adjective clause is a relative pronoun clause and introduces restrictive information.

c. The bursting of the crackers was one reason why the dog couldn't sleep.
The adjective clause begins with a relative adverb (answers the question why).

Adverb clause
7. He kept typing, until his hands ached.
The adverb clause begins with a subordinating conjunction - until

Edit: Missed 'noun modifiers'. Will add the same, and also will add Official Questions instead of random examples. Excuse me for the time being. And will also provide the links to some good posts on this forum