From Halopedia, the Halo wiki
The Warthog Run is a type of gameplay segment in both Halo: Combat Evolved's The Maw and Halo 3's Halo. It involves the Master Chief (or the Arbiter) driving an M12 Chaingun Warthog to escape a Halo's destruction.
Halo: Combat Evolved Warthog Run
In Halo: Combat Evolved, you must enter a vehicle bay and select a Warthog. You must drive around two kilometers down a Class seven Service Corridor to External Access Junction 4C, where you are to be extracted by Foehammer. However, Echo 419 is shot down by Covenant Banshees as she tries to pick up the Chief one last time. After analyzing the UNSC Pillar of Autumn's inventory, Cortana tells the Chief to drive a further one kilometer to Launch Bay Seven, where a Longsword is still docked. As the Chief arrives in Launch Bay Seven, a pile of barrels prevents the warthog from going any further. This forces the Chief to run the last 100 meters on foot. On Easy, Normal and Heroic, you will have six minutes to reach the Longsword and make your escape. However, on Legendary, you have only five.
Halo 3 Warthog Run
After activating the replacement Alpha Halo, the Master Chief and the Arbiter must drive the late Sergeant Johnson's Warthog. They must drive the Warthog to the UNSC Frigate Forward Unto Dawn, which is waiting some distance away, for safety reasons. However, the panels on which the Chief is driving on are being destroyed by explosions caused by the incomplete Halo firing prematurely. When the Spartan reaches the Forward Unto Dawn, he must accelerate to full speed and jump into the frigate's hangar bay. There is no time limit in Halo 3, but if you take too long, the panels will collapse, making it impossible to complete the run. Note that the harder the difficulty, more panels will be destroyed, thus making the run harder than it normally would be.
Changes from Halo: Combat Evolved to Halo 3