Pose to pose is when the animator selects key moments in the animation to get an idea of where the animation will transition to.
A general pose-to-pose animation
Straight ahead is when the animation is done linear and from frame to frame in order. So 1-2-3-4-5 etc.
Pose to pose offers many benefits over straight ahead, including getting timing right, being able to show the director/animation lead where the animation is going before the in-betweens, gives a better overall direction the animation is going and will save time in the long run. Pose-to-pose is the preferred animation type for 3D animation.
Straight ahead is still useful, but the animator has to have a good idea of what he is leading his animation into. A straight ahead animation may also taper and change shape/size if the animator is not careful about each frame. The method can sometimes be quicker, but will be more work if the animation does not turn out correctly.