In popular music, half time is a type of meter and tempo that alters the rhythmic feel by essentially doubling the tempo resolution or metric division. Thus 4/4 approximates 8/8. It is not to be confused with cut time or odd time. Though notes usually get the same value relative to the tempo, the way the beats are divided is altered. While much music typically has a backbeat on quarter note beats two and four, half time would increase the interval between backbeats to double, thus making it hit on beat three and seven (counted out of an 8 beat measure, common practice in half time):
Essentially, a half time 'groove' is one that expands one measure over the course of two.
A classic example is the half time shuffle, a variation of a shuffle rhythm, which is used extensively in hip-hop and some blues music. Some of the variations of the basic groove are notoriously difficult to play on drum set. It is also a favorite in some pop and rock tunes. Two classic examples are the Rosanna shuffle by Toto (Jeff Porcaro on drums), and "Fool In The Rain" by Led Zeppelin.
It is important to realize that while in half time, the feel of notes are chopped in half, but the actual time value remains the same. For example, at the same tempo, 8th notes would sound like 16ths. In the case of the half time shuffle, triplets sound like 16th note triplets, etc. By preserving the tempo, the beat is stretched by 2x.
Half time: notice the snare moves to beats 3 of measure one and two (beats 3 & 7) while the hi-hat plays only on the quarter notes. Play (help·info) Note also, for example, that the quarter notes 'sound like' eighth notes in one giant measure.