There are many different mechanisms by which enzymes increase reaction rates. However, the one thing they all have in common is that their active sites accommodate the transition state product(s) of the reaction they catalyze. So for example Imagine a hypothetical "enzyme" that catalyzes the breaking of a metal bar. In order to break the bar, you must take the straight bar(substrate), bend it(transition state) and eventually it will break in half (products). So when a straight bar finds itself in the active site of the enzyme, interactions between the bar and the active site will make it energetically favorable to adopt a bent conformation (for an instantaneous amount of time because...). Once in the bent conformation the reaction could proceed either way (returning to straight or breaking in half). But because without the enzyme the bar would never find itself in a bent conformation on its own, this reaction is sped up many orders of magnitude. Most if not all enzymes work in a similar way, by stabalizing the transition state of the reaction they are catalyzing allowing very energetically unfavorable reactions to occur (which speeds up the reation rates).