It means exactly what it says. Going back to physics real quick, you have x, which is position; v, the first derivative of x, which is velocity; and a, the first derivative of v, which is acceleration. v, measured in units per second, is the amount of units added to x every second. Similarly, a, measured in units per second per second or units per second squared, is the amount of units added to v every second. A higher value for a, acceleration, will result in greater changes to velocity over a second.
Hopefully that explains it clearly enough. Let me know if you need more explanation.