A Humbucker (as the name suggests) features humbucker pickups, sometimes called humbucking as they can remove the 60 cycle hum that single coils can sometimes produce.
Humbuckers are versatile pickups but generally have a thicker/warmer sound than their single coil counterparts. These pickups can also (depending on their wiring) can be ‘coil split’ which means you use your pickup as single coil for added versatility, though this can have varied results and, in my opinion, can lack the cutting sound and power of true single coils.
Traditional humbucker guitars would be a Gibson Les Paul or a Fender Telecaster 72 Deluxe.
I would recommend Humbucker pickups for fans of;
Slash/Guns n’ Roses
Joe Perry/Aerosmith
Jimmy Page/Led Zeppelin (famous Les Paul and Telecaster player, it may be worth investigating what guitar he played on what songs/albums you a fan of)
Billy Gibbons/ZZ Top
Eric Clapton/Cream
Angus Young/ACDC
Gary Moore/Thin Lizzy and solo artist
Tony Iommi/Black Sabbath
Ace Frehly/Kiss