Concave is the term given to the curve shaped into the bottom of the board, the depth of the concave varies on the board model, waves to be ridden and the shaper:

for a sucky wave like pipeline - a  deep single concave going to a vee out of the tail for bottom turns

for a more rolling wave like sunset - a shallow concave is used with a vee going out of the tail

 

Single Concave

 This  reduces the rocker curve of the board giving it directional speed whilst maintaining manouvrebility because the concave pushes the water down the middle of the board along the concave which acts as a very subtle channel.  The concave is used on most shortboards and some fish.  If the concave is too deep the board gets a bit twitchy although some surfers request a deep concave .

 

Double Concave

Two concaves are shaped into the bottom of the board between the middle of the fins this loosens up the board making it easier to surf the board from rail to rail, jetting the water between the fins.

 

                                                  Triple Concave

The single concave is shaped into the bottom of the board through to a double concave between the fins.

 

The  choice of concave depends upon surfer ability , intermediate surfers normally like a double concave because it makes the board easier to ride, a triple concave is more often requested by experienced surfers.  Team riders like single concave out through the tail with more under the back foot (between the fins)  giving it more control in the curl of the wave and making it more responsive.

But the main thing to remember is that many ingredients need to be right before you put the concave in.  Rocker and rail line have a lot to do with how much concave is put into a board but this will be talked about later.