Keyframes record the transition points in the animation of any element in the scene, such as the motion of an object or the bend amount applied by a modifier. The values at these keyframes are called keys.
The red boxes indicate keyframes, the dotted line shows the interpolated trajectory.
For example, say you have an object representing an elevator that has not been animated; no keyframes (or keys) exist for it. If you turn on Auto Key, go to frame 20, and move the elevator along the Z axis to the second floor, 3ds Max inserts Position keys at the start frame (0 or 1) and at frame 20. The key at the start frame represents the position of the elevator before it begins to move, while the key at frame 20 represents its position after it completes its motion along the Z axis. When you play the animation, the elevator moves from the ground floor to the second floor over 20 frames.