Striving is the -ing form of strive, and it works two ways. As a verb form, it describes the long hard effort as it happens: "she is striving to finish by June", "striving for perfection, he rewrote it six times". As a noun, it means the effort itself, the constant reaching — "a life of striving", "all this striving has made him tired". That noun use is where the word gets interesting, because it usually comes with a feeling attached. Sometimes it is admiring: the honest striving of ordinary people. But very often it hints that the effort is endless and never quite satisfied — a person who is always striving is never at rest, always chasing the next thing. So in writing about work, ambition or happiness you will meet phrases like "the endless striving after money", which is quietly critical. Like strive, it is formal; you meet it in books, speeches and thoughtful articles rather than in conversation. It usually appears with for or after (striving for balance, striving after fame).