We call this exercise the Master Blaster. This exercise will pack slabs of muscle onto your chest in no time, providing that you execute it right and go heavy with the dumbbell weights. This is a classic exercise that is the cornerstone of any respectable mass-building routine for the chest.
The ideal situation would be to have a spotter behind you so that s/he can assist you with the final few repetitions of each so that you can push yourself to the limit. To the limit really means: almost complete failure. If you do this for a few weeks you will notice your chest getting harder, stronger and fuller. That's how good this exercise is!
If your goal is not mass-building then you can do this exercise for toning purposes. In this case, lighter dumbbells will suffice and no spotter is needed.