Ascent venting is the venting of gases during ascent. Spacecraft are typically assembled and integrated with the launch vehicle on Earth, at standard atmospheric pressures. Therefore, any gas that is trapped inside the spacecraft will be at Earth ambient pressure.
During the ascent, the pressure environment in the payload fairing very quickly changes from Earth ambient pressure to near vacuum within minutes. Any gases that are trapped inside the spacecraft must be vented in order to avoid damage to the spacecraft.
However, the vented gases need to go somewhere: they will thus increase the pressure in the payload fairing (or whatever container the spacecraft is contained in, e.g., a space tug or satellite dispenser). This container itself only has limited capabilities to vent the gases. Therefore, the venting needs to be limited.
The limit is set based on the surface area of the spacecraft, i.e., the spacecraft is allowed to vent a certain volume of gas per surface area of the spacecraft.
Volume divided by area is length.