Each enzyme has an "active site". The active site of each enzyme is unique in terms of 3D structure. Each unique active site can be thought of as a 3D surface that is able to bind only a single unique substrate or set of substrates, and it is the shape of the active site that is responsible for each enzyme's substrate selectivity. Most enzymes actually use the same or nearly the same, mechanisms of action; most commonly simple acid-base chemistry is used to catalyse reactions.
It may be difficult to understand, but enzyme active sites are actually thought to bind the "transition state" of the substrate. The transition state may be thought of as a state where the structure of the substrate is literally stretched to be somewhere between the orginal substrate structure, and the structure of the product of the enzyme catalyzed reaction. In other words, the enzyme can be thought of as "pulling" the substrate into a product. In this way, the enzyme lowers the energy required to pass the "transition" state, and accelerates the reaction of substrate to product.
Thus, the structure of the enzyme imparts both its substrate specificity (because only certain substrates will fit into the active site), and its activity (because in binding the substrate, the enzyme lowers the transition energy required for the substrate to form product).
Hope this helped, despite my rambling.
