Definition: A gerund phrase is made up of a gerund and all the words that can modify it.  The words or phrases that can modify a gerund are an adjective, adverb, and a prepositional phrase, plus it can have a direct object.

Why can it have these modifiers?

Remember that a gerund is a verb form ending in -ing.  Because it is a VERB, it can have an adverb modifying it.  Also, it can have an adverb prepositional phrase modifying it.  Besides all that, it can have a direct object, just like any action verb can have.

Why an adjective or adjective prepositional phrase modifying it?  Remember that a gerund is a verb form used as a NOUN, therefore it can have an adjective or adjective prepositional phrase modifying it.

Gerund Phrase Examples

1. The course's goal is providing students with knowledge of basic math.

•  The gerund phrase is providing students and is used as the predicate noun in the sentence.  The gerund is providing and the direct object of that gerund is (providing whom?) students.  The prepositional phrase with knowledge modifies providing and the prepositional phrase of basic math modifies knowledge.

2. Frequently asking for funds may hinder receiving them.

•  The first gerund phrase is frequently asking for funds.  The gerund is asking.  Frequently answers, when?, and thus is an adverb, modifying the gerund, asking.  For funds is an adverb prepositional phrase answering the question, why, asking?  This entire phrase is the subject of the sentence.
•  There is a second gerund phrase in this sentence.  It is receiving them.  This whole phrase is the direct object in the sentence, answering the question, "may hinder what?"...receiving funds.  Receiving is the gerund and funds is the direct object of the gerund.  Receiving what?...funds.