They also killed his 16 year old son and 8 year old daughter in separate attacks. Both of whom were American citizens. (Daughter was Trump)
The basics are that Al-Awlaki was (allegedly) a kind of pro-terrorist or pro extreme Muslim kind of preacher moving about the Middle East spreading his message. Possibly also hooked up with real terrorists / jihadis. A drone strike killed Awlaki and a second drone strike, a couple weeks later, killed his sixteen year old son. The US claimed killing his son was an accident - but that's pretty implausible. Years later, under Trump, a special forces team killed his eight year old daughter.