When you jump, you keep your angular momentum so you will almost follow the Earth around.
I say 'almost' because angular momentum is
[math]L=m \omega r^2[/math] (where m is your mass, [math]\omega[/math] is the angular speed and r is the distance from the centre of the Earth).
So when you jump, your r gets slightly bigger while L (and m) stay the same, meaning that [math]\omega[/math] must get slightly smaller. So you will lose a little angular speed and fall a little behind, but unless you can jump really high this is rather negligible.
A more interesting question would be: what happens if you make a long jump from the equator, heading north?