Crimp is a term used in climbing to describe a certain way of holding onto the rock. The essence of the crimp is that the only part of the hand which is used to gain purchase on the rock are the fingertips. The weight of the climber is loaded onto the rock via the fingertips. There are two distinct type of crimp the open crimp and the closed crimp.
In the open crimp the only inflection of the knuckles happens at the tip most knuckles. Were the hand not to be attached to the rock
it would appear pretty flat, or open. The advantage of this type of crimp is that it causes less stress on the flexor tendons of the fingers, and is therefore less likely to cause injury. The disadvantage is that it is harder to hold on with this crimp and you need to be stronger to use it than you do with the closed crimp.
In the closed crimp the knuckle inflection for this crimp comes at the knuckles closest to the palm of the hand. If the hand were to be apart from the rock it would appear be bent, or closed. Having the bend in the hand so close to the palm gives rise to greater torque on the fingers. This can lead to injury, but on the other hand it is easier to use this crimp than the open crimp.
When one crimps one is said to be crimping.