If you've ever ground plastic or wood, you might notice that at the edge of where you ground, there is fuzzy/frayed material sticking out. That's what a burr is on steel.
Basically what it is is deformed metal due to your grinding at the edge. As frayed material, it is very prone to breakage. If you have a burr on your edge, then when you cut, it will tear off and leave you with a tattered edge.
Thick burrs can usually be felt by running your finger across (NOT along) both sides of the edge. If one side is rough, you've probably got a burr. Another way (more reliable, in my opinion) is to hold the knife in bright light with one side of the blade facing you. Turn it around a little, and if you see a thin "wire" along the edge, you've probably got a burr. You have to check both sides.
The goal of sharpening is to remove this burr so that you have a fine, solid edge, and not one made of this frayed material. This is done by grinding one side to form a burr on the other, then grinding that side to form the burr on the previous side. Then you remove it by doing 1 stroke per side until it's gone. It's much harder than it sounds
