From Halopedia, the Halo wiki
Race is a free-for-all and team multiplayer gametype in Halo: Combat Evolved, Halo: Reach, Halo 4, and Halo 2: Anniversary. The player's objective is to be the first person or team to reach all checkpoints marked on the map.
Halo: Combat Evolved
Halo 5: Guardians
Checkpoints are demarcated by an arrow or, if a player is directly facing one, a flag icon. The maximum number of checkpoints is fifteen.
When a player has completed a lap, information is displayed at the top left corner of the screen, showing the lap number completed and time taken in seconds.
Racing is ideally done in a Warthog, as this allows you a high amount of maneuverability as well as the option of having a gunner to fire at enemies behind whist the driver focuses on reaching the checkpoints, whereas a Ghost or Banshee can only fire in front of you and a Scorpion Tank is far too slow and clumsy to be of use in a Race. Alternatively, racing can be done on a map where there are no vehicles allowed. Racing on close quarters maps like Prisoner or Damnation with heavy weapons can result in highly chaotic game, with players more focused on killing one another rather than actually trying to complete laps. A Moongoose is also preferable if you have a rocketeer.
Originally, racing in vehicles in Halo: Combat Evolved was only available upon the maps Blood Gulch and Sidewinder. However, various updates now mean that racing in vehicles is also available upon Infinity, Danger Canyon, Death Island, Ice Fields, Gephyrophobia and Timberland. A number of these maps - most notably Sidewinder and Gephyrophobia - require for the driver of the Warthog to make difficult maneuvers such as driving up narrow ramps with tight corners. Other maps, particularly Ice Fields and Blood Gulch, have shortcuts that are available to the more experienced drivers e.g. regular racers on Ice Fields will often drive right off the bridge, where the score checkpoint is found, to get to the checkpoint directly beneath it.
Race was removed from the list of playable gametypes in Halo 2—likely due to its unpopularity—and replaced with the new gametype, Territories. Race did not return in Halo 3, although features of both Territories and VIP can be edited to recreate a similar experience. Bungie has created a gametype that is somewhat like Race called Rocket Race, found in the Team Doubles playlist of Halo 3. It is a variant of VIP in which everybody is invincible (except for assassinations) and carries a rocket launcher. The player that is not the VIP is supposed to drive the VIP in a Mongoose to a territory.
Race, however, does make a return in Halo: Reach. A new option provides the capability to turn on Landmines, which bear resemblance to the Trip Mine. Not much else is known about the improvements or adjustments made to the gametype at this time.
Halo 4 variant of Race was introduced to matchmaking as a temporary playlist in December 9, 2013.