Bajrang is a Hindi word which means 'one with a strong frame or a strongly built body.' The word is also commonly associated with Hindu God Hanuman who is called 'Bajrang Bali' too.
Bajrangi is a name (often reserved for wrestlers in the stereotypical world of Hindi cinema) that has the same meaning, strongly built. Bhaijaan is how a brother is called in Urdu with respect. Hence, Bajrangi Bhaijaan would mean 'Brother Bajrangi' where Bajrangi would be a name meaning strongly built and the name is spoken with respect.
Bajrangi Bhaijaan is an upcoming Salman Khan-Kareena Kapoor movie, directed by Kabir Khan.