When an enzyme is inhibited it means that the specific substrate that normally fits in the enzymes active site can no longer bind due to the active site having changed shape or having been blocked.
Competitive inhibition is when the inhibitor is complimentary to the enzymes active site and therefore binds to the active site, by binding it blocks the active site and the substrate can no longer bind to undergo the reaction by the enzyme. This type of inhibitor is concentration dependent, this means that if the concentration of the substrate increases the effect of the inhibitor is reduced as more of the active sites can be filled by substrate.
Non-competitive inhibition is different in that the inhibitor is not specific to the enzymes active site. This type of inhibitor binds away from the enzyme active site and will distort the enzyme active site therefore the substrate will no longer be complimentary. This type of inhibition is not concentration dependent, regardless of how much substrate is present if the active site is changed then it cannot bind.
The effects of the concentration of substrate / the effect of the inhibitor on the reaction is demonstrated in the graphs below. (At this point would use the graphs to visually reaffirm the information)