Overview
I think that few manoeuvres in karate present a greater challenge to students than this block and it's common for even green belts not to have mastered it. In all honesty, performed at full speed, very few students, regardless of their grade, can perform this absolutely properly.
It's a block with numerous possible applications, but if you ask your sensei to demonstrate any of them, chances are, he or she will be unable to. I believe that Mawashi Uke is included in the GKR syllabus to get you used to the idea of flowing, circular hand movements, rather than to teach you a specific block that you will use. I know this much, of the thousands of GKR kumite bouts that I've watched and participated in, I've never, even once seen this block used.
It certainly works as a defence against a side-by-side double punch, and it can be adapted to deflect, and then trap a round kick. It can be done on a big scale, swinging your upper and lower arms (as demonstrated by Kancho in his book "Karate for Everyone"), or it can be done smaller with almost no movement of the upper arms.
The easiest way to learn this block is to break it down into four checkpoints, and check that your arms are in the correct place for each of them. However, the only way that you're ever going to get this one stuck in your head, is practice, practice, practice.
Used in these katas
Karaunfa
Technique
Prepare with your right upper arm tight against your side, elbow bent slightly more than 90 degrees, right hand open with fingers facing upwards in a pushing-away position. The left upper arm is also tight to your side, with the elbow bent slightly less than 90 degrees. The left hand is also open, but this time the fingers are pointing downwards. On both hands, the thumbs are tight to the side of the hand to minimise the risk of breakage.
Swing the right hand downwards in a 180 degree outwards semi-circle until it is just to the left of your groin with the palm of the hand facing right. At the same time, swing the left hand upwards in a 180 degree semi circle until it is just to the right of your face with the palm also facing to the right.
Checkpoint 1 - Are your palms facing the right way? Have you blocked PAST your head and groin or stopped too early?
Continue rotating your arms in the same direction. Swing your left hand down in a 90 degree arc so that it rests horizontally in front of your body at about sternum height with the palm facing upwards. At the same time, swing your right arm up in a 90 degree arc so that it comes to a stop just in front of your left arm, palm facing downwards.
Checkpoint 2 - Are both your forearms horizontal?
Continue rotating your arms in the same direction. Swing your left arm down in a 90 degree arc until the arm is straight down, just to the left of your groin, with the palm facing to the right. At the same time, swing your right arm in a 90 degree arc upwards until it is just to the right of your head with the palm of your hand facing to the left.
Checkpoint 3 - Did you notice that both palms are facing in towards the middle this time?
Continue rotating your arms in the same direction. Swing both arms in a further 90 degree arc (so they should both be sticking out to the sides now). Smoothly retract both arms with your elbows tucked in, until your open hands are pressed against the sides of your ribcage at about sternum height, right fingers facing downwards, left fingers facing upwards. Breathing out, tensing your stomach and moving with tension, extend your arms in front of you as though pushing a heavy weight away. Stop when your upper arms are vertical by your sides.
Checkpoint 4 - Your lower arm should be in the same position as if you were doing a short punch, but without the elbow tucked into your stomach. Right hand fingers should be facing downwards, and left hand fingers facing upwards.
Common mistakes to avoid
Remember the checkpoints. Are your hands facing the right way? Don't lose it when you start to go faster.
Don't push your arms all the way out in front of you at the end - you're not doing a Diana Ross impersonation!
Did your hands actually pass in front of your head and groin at the checkpoints? This is a very common mistake as experienced students perform this block with speed. Don't truncate your block just because you're going fast - your attacker won't stop short of your nose or groin because he's moving quickly...
If you find your hands bashing against the inside of your elbows, or each other as they pass each other, simply move your elbows further apart at this stage. Problem solved. Easy!