Powershielding is a difficult shielding technique in SSBM. When used, any incoming attack is blocked with no damage done to a character's shield, and projectiles may also be reflected. Because powershielding is technically a shield, it is ineffective against grabs.
Powershielding is done by quickly and fully depressing L or R so that the incoming attack is inside the character's shield. If done correctly, there will be a white flash and a distinctive (though somewhat hard to hear) sound. If the timing is slightly off, then the attack may be blocked by a lightshield, a normal shield, or it may not be blocked at all.
CPU players, especially level 9s, use powershielding a lot. Human players don't use it as much simply because of the reaction times and precision usually required. As such, powershielding often comes as a surprise and can momentarily disrupt a match.
Something not completely understood is how Yoshi's egg shield sometimes powershields attacks even when the shield is already up.