After run oil is just what the name implies. Oil that you put in the engine after you run it. You do this at the end of the flying day.
First pull the fuel line off the engine, install the starter battery and start/run the engine until it quits. This gets all of the nitro out of the engine which can be corrosive.
After this, remove all of the starting stuff and put about a teaspoon of after run oil in the wide open carb intake. Turn the plane over if you need to due to an inverted motor. Flip the prop through a few times to circulate the oil (do not use starter) and leave a nice coat of oil on the bearings and engine interior.

ATF (Automatic Transmission Fluid) can be used as after run oil and is much cheaper that the LHS. One quart will last a long time. Just put a little in a small bottle and take it to the field with you. First start the next time may be slightly smokey but it will be OK. There are other oil mixes that others will chime in here with, most are fine.