Increase in Enzyme concerntrations affect on a reaction
Well in any enzyme catalyzed reaction you have an enzyme and a substrate (that is the substance that the enzyme acts on). So for example, if you had the enzyme amylase which digests starch your substrate would be the starch and you would test the effect of enzyme concentration on the rate of reaction by keeping all other factors including the concentration of starch the same and simply increasing the enzyme concentration.
The enzyme binds to or somehow interacts with the substrate to speed up the reaction. There are certain sites on the substrate that the enzyme will act on. So as you increase the concentration of enzymes it increases the number of successful collisions and so to a point the rate of reaction is directly proportional to enzyme concentration and the higher the concentration of the enzyme the faster the reaction.
However, at some point this will 'plateu' - that is it will 'level' or reach equilibrium where the reaction reaches its maximum rate regardless of the enzyme concentration because all the sites on the substrate are 'full' and so the excess enzyme is just floating around doing nothing because it has nothing to react with.
Hence, if you were to draw a graph of the effect of enzyme concentration on the rate of reaction with enzyme concentration on the vertical axis and rate of reaction on the horizontal axis then it would be a diagonal line going straight up through the origin until it reaches a point and then its a 'flat line'.