Internal clearance being C3 means that the bearing has room for expansion if needed between the races of the bearing. Whilst holding the outer ring and moving the inner ring in a radial movement you will detect a little amount of play between the two rings. All standard clearance bearings have this movement, it may only be a small amount of movement but is controlled by international standards. C3 means the bearing has more clearance than standard.

In motorcycle engines C3 clearance on bearings is specified where a cold start up application may cause the balls to heat up quickly, the heat needs to go somewhere. Some of the heat gets passed through the outer race to the housing and the inner race to the shaft, this causes expansion which closes up the clearance in the bearing. If this clearance was not allowed for then the bearing would not have room for expansion and lead to bearing failure.

It is never advisable to replace a bearing with one having a lower initial clearance. But it is usually safe to substitute a larger clearance when the desired clearance is not available.