If you've had piano lessons, you may well have had teachers who told you to "curve your fingers." You may have been told to imagine your fingers curved around a ball, such as a tennis ball. There are beginner books, for both children and adults, which show a picture of how this should look.
The problem is, it's just plain wrong.
Challenge anyone who tells you to curve and ask them to explain why. There just isn't any good reason. Try playing an octave, or a chord spanning an octave with four notes, and you'll see you can't do it with curved fingers. The hand (the palm, actually) must open up to be able to span that distance. Look at Chopin's first etude in C major; the entire piece consists of arpeggios which span a tenth, and the whole thing is meant to go at lightning speed. There is no way to do it with curved fingers.
If your piece requires loud dramatic chords, of course this has to be accomplished with the arm (despite what some will tell you.) But if you come down hard onto curved fingers, the joints of the finger take all the impact and it can be dangerous for the joints.
Instead, you want to have the natural curvature of your hand. Lay your hand palm up (prone) on your lap, and your hand will form it's natural curvature. Move your hand to the piano without changing anything; this is how you should play. Some people naturally have more curvature, some have less. No one has a completely flat hand, and no one is naturally curved as if over a ball. You may need to flatten (open) your hand even more to play a ninth or tenth. Watch a video of the late Vladimir Horowitz; you'll see he had practically flat fingers, yet he had huge technique.
With curved fingers you contact the keys on the tip of the finger. This is why you'd hear the clicking of your nails unless you keep them extremely short. (See my post "Can Pianists Have Nice Nails?) But if you have more of an open hand, you contact the keys with the pads of your fingers, which, as that term indicates, gives you more padding. It is much more comfortable and better suited to take the impact of loud playing, and you won't hear your nails clicking.
As with many other old ideas about piano technique, curved fingers orginated in the days of the harpsichord and early pianos, which were very different from our modern piano, and the music being composed at the time was also much less demanding. Curved fingers is another example of what I call a "300-year-old idea."