The basic idea of a bearing is something that reduces friction between two rotating items. In a yo-yo context only ball bearings and sleeve bearings are used, but sleeve bearings are only made of one part so we will look at ball bearings here.
A ball bearing reduces friction by having balls inbetween the two moving parts. The innermost metal ring is referred to as the inner race, whilst the outer ring is referred to as the outer race. These two races have a groove on the inside to hold the balls. A typical bearing has eight balls, although some smaller bearings only have six. These balls are held in place by a 'ball cage', which ensures the balls stay in the right place.
Less important parts
As well as the working part of the ball bearing there are shields and c-clips to protect the insides and reduce the amount of dirt and grease that gets into the bearing. The shield is a flat, circular piece of metal which sits between the inner and outer race inbetween the balls and the outside world. There are two shields, one on each side of the bearing. The c-clips are there to hold the shields in place, and sit between on top of the shield next to the outer race. Due to the size of yo-yo ball bearings the c-clips are often very hard to spot and remove.
These are not essential to the function of the bearing and so some yo-yoers do not use them. The only disadvantage of not using them is that the bearing will need to be cleaned more often as the lubrication will escape and dirt and string lint will get inside more quickly.
Above you can see a completely disassembled Dif-e-Yo KonKave bearing. Please note that you cannot take a bearing apart like this and put it together again. For cleaning, you only need to take off the c-clips and shields.
From left to right: in the bottom left corner you can see the two shields. In the top left corner you can see the c-clips. In the centre you can see the ball cage, with its eight gaps where the balls are positioned. In the bottom right corner you can see the balls that are inside the bearing. Although only five balls are pictured a konkave bearing actually has eight. Above the ball to the left you can see the outer race. Note that since this a konkave bearing the outer race is curved so the string is centered. In the top right corner you can see the inner race. Note the groove on the inner race which the ball run along. There is a corresponding groove on the inside of the outer race for the balls, which you can see if you look carefully.