Q:

What does "vt", "vpr" and "vi" mean when referring to verbs in a Spanish dictionary? 

Does anybody comprehend these abbreviations in the image, used in Oxford's Essential Spanish Dictionary? 

It says:

venga|nza f revenge.  ~r vt avenge.  ~rse vpr take revenge (de, por for) (en on).  ~tivo adj vindictive. 
veni|da f arrival; (vuelta) return ~dero adj coming.  ~r vi come. 

A:

It is telling you that:

vengar is a transitive verb (vt - verbo transitivo) which takes an object, to avenge someone. 
vengarse is a pronominal verb (vpr - verbo pronominal) 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. 
venir is an intransitive verb (vi - verbo intransitivo) which does not take an object.  You just come, you do not come something.