Here are the relevant quotes from the rulebook:
"Each turn is ten minutes except during combat where there are ten melee rounds per turn, each round lasting ten seconds" (pg 9)
"There are ten "rounds" of combat per turn. Each round is ten seconds, so a combat turn is shorter than a regular turn, but results in at least as much muscular fatigue" (pg 20)
However the rulebook doesn't specify what the purpose of tracking "combat turns" is. Why not just track rounds during combat? Combat movement per round is given on pg 20, so it's not like the "combat turn" is needed for movement.
The main thing that "combat turns" would seem to apply to is spell/magic (i.e., potion) durations. However, the shortest spell duration is 2 turns, which is 20 rounds, longer than most combats. Once combat is over, the tracking of time shifts back to normal, which means the remainder of the spell duration then shifts back to "normal turns" until it ends. So what the different turns are used for is tracking how much of your spell turns are used up by melee rounds (10 combat actions = 1 turn) vs exploration (1 movement or search = 1 turn).
As an example, Mar Pres the Conjurer, a third level magic-user, casts the spell Enlargement on fellow party member Tensho the Warrior during the 1st round of a combat with an ogre. This spell has a duration of 1 turn plus caster level, so Tensho will remain enlarged for 4 turns. If the combat is 10 rounds or less, 1 turn of the spell would be used. After combat is over, 3 "regular turns" (30 min) would remain. If combat went between 10-20 rounds, a second "combat turn" would be used, so after combat Tensho would only remain enlarged for 2 more "regular turns" before returning to normal size.
In the module B2, the original version of which was written specifically for Holmes Basic, Gygax gives some useful advice on the "combat turns":
"If fighting should occur, the time reference shifts to a melee turn which is subdivided into ten, 10 second melee rounds. The concept of a melee turn is designed to simulate the quick exchange of blows in combat. For the sake of convenience, a DM can consider one entire melee turn to equal one normal turn (that is, 10 minutes), no matter how many melee rounds the combat took. The extra time is spent recovering one's breath, checking for woulds, re-sharpening blunted weapons, etc." (pg 4, section TIME)
This is practical because it results in the actual time length between combat turns and normal turns being the same, and fits with Holmes statement that combat turns result in the same amount of fatigue as a normal turns.
[the above is adapted from several recent posts in a thread on OD&D Discussion]