Constructed of a set of magnets that is wound, single coil pickups tend to have a brighter sound with more attack.  The pickup has high output and is designed to articulate the subtleties of the strings. The downside to a single coil pickup is that they tend to have increased background noise or interference (e.g. from a computer monitor).

A humbucker pickup is constructed of a set of magnets that is wound twice (in opposite directions) to cancel out the “hum” or interference that single coil pickups can produce.  Typically guitarists will describe this as a ‘warmer’ sound with a mid-range focus.  There is slightly less string articulation but noise will be lowered considerably.