From e4, an Alfil can reach c6 (even if there is something on d5), g6, g2, or c2; but notice that an Alfil can never get to 56 of the 64 squares on the board...
By itself, the Alfil is too weak a piece to be of much interest, but its power can be combined with the powers of other pieces to make new and interesting ones. By itself, it is hardly worth more than a Pawn, but in combination with other pieces it is worth half a Knight, more or less.
The funny notation for this is simply the letter A, because the Alfil is one of the basic geometric ingredients used in the recipes for other pieces.
In order to mate in the Pawnless endgame with King and Alfils versus King, you need lots and lots of Alfils to cover different squares!
It would be possible to have an A7 piece which would be to the A what the Bishop is to the A. This Alfil-rider piece could go from a1 to c3, and if c3 was empty it could continue its move to e5, and if e5 empty, and so on.