Burr grinders are a step up from your run of the mill (no pun intended) flat grinder you typically have at home for grinding fresh coffee beans. The key to great espresso crema and proper extraction is to acheive consistency in your grind - that is where the burr grinder comes in.
Flat blade grinders have two issues, they generate a lot of heat as they grind the beans and they produce an inconsistent grind due to the way they perform the grind. Heat means a loss of oil and aroma in your beans - not good if your paying for premium beans and are seeking quality. Inconsistent grinds means while they may work in a drip pot or potentially even a french press, they won't deliver the results you're looking for in an espresso machine.
Burr grinders typically contain two sets of blades, generally in a cone shape that crush the beans between the two sets of blades. The gap between the blades is set by the user and can control the coarseness of the grind. This process means less heat as well, the blades can move much more slowly because they are crushing the beans - not just blending them into obscurity!