This is a verbal that ends in (ing) and functions as a noun.
Ex: Traveling might satisfy your desire for new experiences. (Traveling is the gerund)
Ex: They do not appreciate my singing. (singing is the gerund)

Gerund Phrase: Will begin with a gerund ending in (ing) and might include other modifiers. Gerund phrases always function as nouns, so they will be subjects, subject compliments, or objects in a sentence.
Ex: Eating ice cream on a windy day can be a messy experience if you have long, untamed hair. ( is the gerund phrase)
Ex:I hope that you appreciate my offering you this opportunity. (offering is the gerund)(my is the possessive pronoun modifying the gerund)(you is the indirect object)(this opportunity is the direct object)