Reactions involve collisions between molecules.  If you increase the kinetic energy, you increase the frequency of collisions and the rate of reaction. 

Enzymatic reactions also require the substrate molecules to be correctly aligned when they collide near the enzyme's active site; if they are not aligned just right, the molecules will bounce off each other and no reaction will occur. Perhaps only 1 collision in 100 or 1000 is aligned exactly right.

Each enzyme has evolved along with its substrate molecules.  Not only do their shapes match, but also the polar covalent bonds on their surfaces match.  As the substrates approach the active site, hydrogen bonds begin to form and pull the substrates into perfect alignment.  These hydrogen bonds cause the substrates to firmly bind to each other and to the enzyme, and they cause the enzyme to "grip" the substrates in what biochemists call an induced fit.  This induced fit can bend and twist the substrate molecules in a fashion that further facilitates the reaction.

An enzyme lowers the energy barrier by controlling the alignment as the substrate molecules as they all collide, such that each collision causes a reaction.  

Baseball Analogy: Assume an invisible force field could be created around the batter.  As the ball flies towards the batter it enters the force field and is guided to a point right over home plate.  As the batter swings, the bat enters the force field and is guided to exactly the same point.  At the moment of contact, the force field produces a perfect alignment such that the ball is hit at a 38 degree angle up and out of the ball park.