do your best; go for it; hang in there
A common encouraging interjection used to cheer someone on, similar to 'good luck' or 'you can do it'.
Good luck on your exam.
Go for it in tomorrow's match!
頑張って has a softer, more polite request-like feel, while 頑張れ is the blunt imperative form used bluntly among close friends or as a rallying cheer.
The te-form of the verb 頑張る (がんばる), which originally meant 'to insist on one's own opinion' or 'to be stubborn', later shifting to 'to persevere'.