A very simple explanation. This assumes the wind is coming from your left while you are standing at the pilot station facing the runway.

1.) Taxi to the end of the runway to your right and turn the plane around so that it is facing into the wind,
2.) Takeoff and fly straight out for a few seconds to gain altitude (upwind leg),
3.) Turn right 90 degrees, flight straight a few seconds (crosswind leg),
4.) Turn right 90 degrees and fly straight until you are past the end of the runway by a few seconds and
at this time you are also cutting back on power to start decending towards the runway (downwind leg),
5.) Turn right 90 degrees fly sraight and just before the extended centerline of the runway (base leg),
6.) Turn right 90 degrees. The turn should be timed to lineup with the extended centerline of the runway so you are actually making this turn before you get to the extended centerline and still decending to land.

You do not have to cut power to land on the downwind leg. You can just make all of the 90 degree turns and just fly straight down the runway. This is called practicing approaches. You can also land and let the plane roll a few feet then power up and takeoff again, also known as a touch and go.

You are basically drawing a rectangle in the sky. That is what is known as flying the pattern and should be second nature before solo. As also was described it can help cut down on accidents.

I have given you the full scale version but it applies equally well in R/C