。
Don't neglect your daily duties.
Literal
Every-day [possessive-の] duties [object-を] neglect [prohibitive-な].
怠るな uses the prohibitive particle な directly after the dictionary form — a terse, authoritative prohibition. 務め ('duty/obligation') is distinct from the homophone 勤め ('employment'): 務め emphasizes moral or role-based responsibility. The sentence has a proverbial ring.