Green’s Dictionary of Slang

1. sexually aroused.

1961

C. Cooper Jr Weed (1998) 127: Fresh home and hard-on, he’d found the street and apartment.

2. tough, aggressive.

1957		Kerouac letter 21 July in Charters II (1999) 55: Don’t be bugged by what Cowley wanted put in [...] about ‘intellectualism’ of you & Bill & Joan as against Neal’s hard-on hungry purity.
1988		D. Woodrell Muscle for the Wing 98: Tell your hard-on brother what you seen over at Frechette Park.