"Wing".

[SirDanley]

Apparently my board has one, as described elsewhere around here...

Wing

The wing is really not a tail shape but more of a rail shape. It can be seen as the bump in the rails just in front of the front fins.

Theoretically, what ought be the purpose to this, as compared to a board without them?

[vandangos]

its to bring the tail in on a wide board (fish) so you can turn tighter. it allows more width in the board whilst beng able to turn.