Acceleration is velocity over time, and velocity is displacement over time. (This explains why time is squared.) As for the units, physicists (as well as pretty much any other kind of scientist) rely on SI units, which are the units generally accepted by scientists world-wide. Meters are the SI unit for length, and seconds are the SI unit for time.
This is because to find acceleration, you must divide velocity by time. Velocity is measured in meters / second, and time is measured in seconds. So, when meters / second is divided by seconds, the units become meters / second squared.
