Achievement hitching is when the game momentarily freezes before giving you an achievement. After completing the appropriate action for the achievement, the game will look to see if you've unlocked an achievement or not. The phase during which the game decides if you've unlocked an achievement or trophy is when the game temporarily freezes. This freeze can end with the player starting from where he had left off or the game can skip forward.
Achievement hitching was a recurring problem with the PS3 version of Fallout 3 where the game would take its time between when you performed the correct action to unlock the trophy and when the trophy was actually given to you. During this time, the game would freeze for several seconds before working again. This problem was probably due to a bug between the game and the PS3 hardware as the game would also freeze when friends came online or sent the player a message.