what are climbing slings and runners for
and cords and webbing for??

First cords & webbing r usually tied into a loop, kind of a make shift runner/sling. All of these can be used for multiple purposes, but the most specific use is to extend the distance between gear & the rope.
Top rope: They can be used to help create top rope anchors by lasoing trees or boulders, or extending between the gear for the anchors & the edge of the cliff.
Sport lead climbing, they can different lengths can be used between carabiners to create longer quickdraws so there is less rope drag. Also when u r cleaning a climb (removing all of the quickdraws) they can be used to clip the climber directly into the anchors so they can take the remaining quickdraws off of the climb, then rapel down.
Trad climbing they can be used the same way as sport climbing only u would attach them to the protection so there is less rope drag & less likely for the rope sliding through the carabiners to pull the gear out of the rock. You can also use them to lasso a chickenhead rock, or passing it through a tunnel like opening & using a girth hitch instead of placing a piece of gear.
You can also use them around ur body while u r gearing up for a climb. Use one to carry gear along with ur gear loops on ur harness.
Cords (cordellet) can also be used in situations where u need to climb the rope itself, escape a belay, or as a backup for hauling.
All of this has so many uses. Unfortunately, without being able to show u most of this is going over ur head. If u can find a local that climbs outside, they should be able to explain all of this in greater detail.