Somewhere in my mind, the meaning of it is saved. But I can't recall exactly what it means.

A handy guide to the terminology of derivatives and integrals of the distance from an object to the origin (displacement or position):

First derivative is speed.
Second derivative is acceleration.
Third derivative is the change in acceleration (Jerk).
Fourth derivative is sometimes called jounce.

First integral is absement.
Second integral is absity.
Third integral is abseleration.
Fourth integral is abserk.
Fifth integral is absounce.

If want the integral of acceleration, it's speed (velocity is a vector, integration returns a scalar).

Cyano's correct, it's velocity.

One easy way to look at it is that integrals (area under the curve) are basically multiplication. I mean, when you write an integral for this, it's [itegral sign]a(t)*dt. So, it's really just acceleration * time which equals velocity.

On the other hand, derivatives are division. So the derivative of velocity with respect to time is velocity/time = acceleration. Again, dv/dt shows this pretty well.