When you are cutting a ductile material (most particularly metal) on a high-speed machine, the chip coming off the workpiece may not be a chip so much as a string. As the tool moves along the surface, it knocks off a long 'peel' of material; if a tool is not designed to prevent this, that peel of material can remain in one long, continuous strip, which can form long whips or tangles akin to steel wool. These can then whip around to foul the cut, take out your eye, scratch up the finished surface, or do other mischief.
The chip breaker is a small bump on the tool head just behind the cutting edge, forcing the emerging chip to take a sudden, sharp turn. The optimal angle and distance from the cutting edge will vary depending on what you are cutting, your depth of cut, and what speed you are cutting at, so there is a very large variation in what exactly a chip breaker looks like. Most often, it will be a small shoulder cut into the tool or a small plate attached just behind the cutting edge.
While there is not necesarily such a thing as 'the correct chip' to aim for, in general chips should look something like macaroni rather than spaghetti. Chip breaking is most often a concern when working on a lathe or a mill; drill bits may have chip breakers, but long chips are less likely to foul a drill, and in fact you might rather have the material out of the bore in a long strand than have it collect in small chips around the bit, so most drills do not use chip breakers.