あげます is a verb for "giving". It is used when a person, the subject of a sentence, gives something to another person.
小林さんは マリアさんに はなを あげました。
Mr./Ms. Kobayashi gave Maria flowers.
The verb あげます can never be used when the speaker わたし (たち) or the speaker's "in-group member" is the receiver of the object. See Structure 5 for the pattern in which the speaker (i.e., the first person) is presented as the receiver, when s/he is not the subject of the sentence.