"A pat on the back" is a gesture that someone gives you if they are proud of something that you have done. People do not always literally do this, but referring to the act has become a way of saying that you are giving someone encouragement.

So you could say "I always give my staff pats on the back when they finish projects", or "Dave deserved a pat on the back for finishing his work on time".

Another way is to say you gave someone an "attaboy". That is a bit dated though. It's the kind of thing my father would say, but I probably wouldn't.

Michael's answer is perfect.

I would also say that "a pat on the back" can be physical or verbal.

Athletes congratulate each other when they score a goal by patting each other on the back (physical congratulations).
Adults congratulate children and other adults by giving/saying a verbal congratulations. Employers do the same with their employees (verbal congratulations).

Some employees, who do good work, would rather be recognized by their employer by receiving a verbal pat on the back than receiving a small amount of money (verbal appreciation).