PUSHUPS VARIATIONS...

Pushups work the chest (pectoral) musclels, shoulders (deltoids), arms (triceps), core, legs, glutes, back, lats... most of your whole body.  Pushups (pressups) are one of the best all time and all rouind bodyweight exercises for three reasons.  The large number of muscles they work.  You can do them just about anywhere with no gym equipment.  Because of the great variety of pushups that can be done it gives a great total (whole) body workout.

Below you will see listed most of the pushups done in the video with with a few extras, some brief notes about which muscles they may give special focus to.  Note: all pushups will give the chest muscles, deltoids and triceps a good workout if done properly.  However, depending on the pushups variation (style), you will get a stronger focus on certain muscles as identified below... 
 
Wide Grip (Wide Hand Position) Pushups - more shoulder and outer chest
Close Grip (Narrow Hand Position) Pushups - more triceps and inner chest
Decline Pushups with wide grip (hand position) - decline works the upper chest
Decline Pushups (hands on ball, 1 foot on bench) - more core and serratus anterior
Incline Pushups (feet on floor and hands elevated on a bench) - works lower chest
Diamond Puahups - big hit on the inner chest musles, also good for triceps
Archer Pushups - brings in the lats... good progression towards one arm pushups
One Arm Pushups - triceps, chest, shoulder
Tiger or Spinx Pushups - major tricep activation, serratus, and not as much chest
Cross Triceps Extension Pushups - major triceps again, serratus, and a bit more chest  
Dumbell Pushups - narrow or wide, it gives more extensive activation of muscles
Feet Against Wall Pushups - Shoulders, Serratus, Triceps, Chest, Glutes, Abs, Legs...
(This last pushups variation is the hardest pushup you'll see in this video).