For an overall compression definition see Compression Damping
The term low speed refers to low shaft speed and is a common control found in higher end forks and rear shocks. Low speed movements are most often perceived as pedal-bob, issues with diving through travel, and having the ability to stay up in your travel.
With no low-speed damping your suspension will very easily soak up every fluctuation in terrain (roller, small bumps, shift in weight, pedal-bob, etc.)
Adding low-speed compression damping will make it harder to “break-away” from your resting position at the top of your travel and keep you up in your travel for the bigger hits. An increase in low-speed compression will also allow the rider to pump through terrain features, not dive through travels through harder cornering, and reduce pedal-bob but will also sacrifice small bump compliance.
Finding the middle ground between efficiency and bump compliance is the challenge.