An Autopilot Route is a sequence of systems to travel in order in order to pass by certain systems and/or reach your intended destination. Adding waypoints to non-adjacent systems will create a path to that system that satisfies certain specified properties (eg. shorted route, safest route, ec).
If Autopilot is engaged, then the ship travels through these systems automatically; however, it does so very slowly and dangerously. Compared to manual jumping, Autopilot is slow to initiate the jump, and does NOT jump to 0km away but rather 10km away from the waypoint before flying towards it and, in the case of a stargate, making the next jump. This leaves a large window of opportunity for hostiles to attack you before you arrive to the waypoint. For this reason, Autopilot should never be used under any circumstance. Even if you were in an NPC corp in Hisec, suicide gankers excel at taking down autopiloted ships and plundering their wrecks.
While using Autopilot is a terrible idea, you can always use the Autopilot Routes to manually jump to your destination. Unlike Autopilot, you can initiate warp faster and you can jump to 0km from the waypoint; in the case of stations and stargates, you will enter/jump before the enemy gets the opportunity to attack you.