Suppose you have an important Pawn at d4, attacked by 3 enemy pieces and defended by 3 friendlies. None of the defenders dares move away, because doing so would lose d4; and so all 3 are tied down and relatively immobile.
If you add another defender, then any one of the four defenders is free to move away -- instead of 3 immobile pieces, you have 4 mobile ones!
A single overprotection gains the ability to move but not capture as a Wazir, Ferz, Barc, Crab, Alfil, or Dabbabah, in that order. For example, the Rook already can move as a Wazir, so instead it gains the ability to move as a Ferz; or a Queen already moves as W and as F, so instead it gains the ability to move as a Barc.
Two overprotections gain the ability to both move and capture as the first available of W, F, Barc, Crab, A, or D.
Three overprotections allow the heavily-defended piece to move as the second available thing from the list (in addition to moving and capturing as the first), and four let it move and capture as the second.
And so on...
When calculating overprotection, do not count attacks and defends added by overprotection, only those resulting from the pieces' base movement. Otherwise, you can get into all sorts of trouble, such as endless loops.
The added power is temporary and dynamic. Moving off the overprotected square loses the extra power, but landing on an overprotected square immediately gains power. Therefore you can destroy your opponent's overprotection by moving your attacker away.
Pawns may not gain as much as other pieces, because they already have part of the powers of W and F.
Notice that a piece which is defended many times, but not attacked at all, gains no power. Therefore, the King can gain power only when he is in check! And therefore, it is possible to imagine a position where checkmating your opponent also checkmates you! (It would be an illegal move.) How? If the enemy K is defended several times (but of course not attacked) so that when you attack the enemy K it becomes overprotected and gives check to your nearby King.