It is telling you that
vengar is a transitive verb which takes an object, to avenge someone.
vengarse is a pronominal verb form which always has the pronoun attached and which has it declined to agree with the subject. In this case it means to take revenge either for (de, por) or on (en).
Pronominal verbs are explained in this Wikipedia article https://es.wikipedia.org/wiki/Verbo_pronominal (in Spanish) and are usually referred to by English speakers as reflexive verbs although the truth is more complex in general.