To vet someone is like performing a background check on them. You look at what they state, or the qualifications that are needed for a position, and you VET them to make sure that they qualify for the position, taking everything into account. Mostly done for appointed positions and high profile jobs....mainly to make sure that they know what they are doing and that there can be no repercussions from their past.

or it's an animal doctor....

A doctor who is trained how to diagnose and treat animals or

someone who has served in their country's armed forces.

I suspect the first is more correct for your question.