Lane priority means, you have priority to leave the lane and help somewhere else by having control over the lane. That means, if you can push the lane into the opponents tower, without them being able to stop it, you have lane control and thus priority.

This gives you several advantages:

You have the opportunity to make roams and ganks into other lane without losing too much The opponent cannot follow as they are stuck under their tower. You don't lose much farm ,as it takes time until the opponent can push out again It gives your jungler more freedom, as you are able to react faster than your opponent to any encounters with the enemy jungler You have the opportunity to sweep wards or place deep wards without losing anything.



However be careful, if you have lane priority, you also often play quite a bit forward and thus are easier to gank, which is why the jungler often plays around lanes, which have control.