In the most basic terms ablative lasers remove or break down skin cells, mostly in the outer layer where you shed old skin cells. Non-ablative lasers do not remove any of the surface skin cells. Instead, they typically work by more gently heating into the deeper layers to induce new skin growth and collagen production.
Ablative treatments come with some more down time and more potential for side effects if performed inappropriately. However, the results are typically more impressive than with the less invasive non-ablative options. Non-ablative treatments usually require a series of several treatments to gain modest results.