Latin for "Don't despair!" or "Keep your chin up!".
Literally, "nil" is short for "nihil" ("nothing") and "desperandum" is a gerundive meaning "things to despair for" or "things to lose hope of". The copula "est" has been elided, but you can put it back, si tibi placet, to yield "nil desperandum est".
Horace first said this in his 7th Ode, published in 23 B.C. or 731 AUC.