Adjectives and adverbs are both words that describe something. If anyone has ever asked you to describe something in detail, you probably used some adverbs and adjectives along the way.
The difference between adjectives and adverbs is that an adjective modifies a pronoun. For example: They had worked all day and they were tired. The adjective, 'tired', tells more about the pronoun 'they', whereas an adverb modifies adjectives and other adverbs.
Because in the sentence the verb "is" is describing that a person "is from a place". In this case the sentence is saying that "My boyfriend is Colombian" but not that "he is in Colombia". Therefore the correct option is to SER.