Together with the overhead press, the bench press is an important upper body strength movement.
It develops the anterior deltoid and pec musculature like no other exercise. Dumbbell advocates my argue that their piece of equipment is "better". However, the barbell bench press allows for infinite progress, and you start earning the real big bucks in that movement once you hit your performance for sets of five past your own bodyweight and beyond. So in the long run, you're much better off building up your bench press. Nothing worth having has ever come easy.
Why do we want to keep the butt down in the bench press?
One: greater range of motion in the movement.
If you lift your hips off the bench, the distance from the chest relative to the bar shortens.
That means, shorter range of motion in which the muscles get worked. That means, lower overall muscle activation and thus lower strength development as well as growth.
Two: standardization. Lifters with longer legs have a clear advantage by being able to lift their butt higher and more efficiently than lifters with relatively shorter legs. If we teach lifters to keep their backside down, everyone starts from the same level.
Three: fewer variables to control. For strength, we want to exclude as many "noise" in the lift as possible. That is, things like momentum or extra body part involvement are not desired in the movement.
Another tip: get a spotter to watch you bench press, or video yourself. And count only the reps where you have your backside on the bench.
Happy benching!