This image pretty much sums it up. When ever I try to pose the head, legs, arms, etc. the model warps like this. Oddly, the mesh only warps in this direction, front to back. I hit G or R to pose it and it does this on both. I'm pretty new to blender.
You've probably scaled your armature on the Z axis in Object mode, so apply its scale in Object mode (or you may have stretched your bones in Pose mode but probably not).
You probably wanted to scale your character on the Z axis but it's not the way to do it, you need to select your mesh and scale it in Edit mode to do so, then change the bones size in Edit mode as well.