A "double shaft motor" has "two shafts" that exit the motor case.
If you turn the motor on so the shaft spins and keep the motor case rigidly bolted in one position, there is one place where you can stand and see one shaft sticking out of the motor and pointed directly at you and turning clockwise.
Meanwhile, there is another position someone else can stand on the opposite side of the motor; that person sees the shaft sticking out of the motor and turning counterclockwise.
(Some people prefer to think of those two shafts as two ends of a single shaft -- they have a good point, since both shafts are part of a single rigid cylinder of metal).
(double shaft motor http://www.myrcstation.com/webshaper/store/viewProd.asp?pkProductItem=5797 )
A "single shaft motor" has a shaft that only sticks out in one direction.
Often the only difference between some "double shaft motor" and a closely related "single shaft motor" is how far out the "other" shaft sticks out.
Often there is a hole in the case of a single shaft motor, where the other shaft would have stuck out, if it were a double shaft motor.
In the single-shaft version of that motor, you can typically you can see, through that hole, the end the shaft turning -- but the shaft doesn't stick out far enough to do anything useful.
Often people put some sort of drive wheel on one shaft of a double shaft motor, and put a position-measuring encoder on the other shaft.
Most applications only require a single shaft motor.
Often such single-shaft applications work fine with a double shaft motor (with the unused shaft not connected to anything).
So when I see that it's the same price either way, I generally choose a double shaft motor -- that way I can use that motor in both single-shaft applications and double-shaft applications.
.... battery operated (BO) motor ...