If a reaction mixture is at equilibrium, if you add some more reactant, according the Le Chatelier's principle than the reaction will change in order to "counteract" the change. That is to say is will shift to partially "undo" the change you have made. Therefore if reactants are added, the reaction shifts to "remove" some reactants. This can be accomplished by shifting towards the products and forming more products. Conversely if you add products, the reaction will shift to reactants to counteract this change.
While Le Chatelier's principle is handy (and correct), it can often give the wrong impression especially as one tries to explain it. It makes it seem like the reaction mixture is making some sort of decision of what to do. Moreover, without understanding the underlying ideas you can arrive at the wrong answers. This first idea of adding (removing) products or reactants is not different than Q vs K. When a reaction is at equilibrium, the mass action expression (the concentrations of the products divided by the concentration of the reactants) has a value equal to K (Q = K). If you change those concentration you will no longer be at equilibrium (Q ≠ K).
\[Q = {Products \over Reactants}\]
Adding reactants (or removing products) will lead to a situation in which Q < K (you're dividing by a bigger number). Adding products (or removing reactants) will lead to Q > K (you'll have larger number on top of the mass action expression).
It is important to make this connection since pure liquids and pure solids have activities that are one (they don't appear in the mass action expression). Thus if you add more of them they will not affect the equilibrium at all. Solubility is a situation like this. If you have a saturated solution and you add more solid nothing happens (the reaction does not shift to the right even though you have added more reactant). You need to change the concentrations or pressures in the mass action expression to affect the equilibrium.
Finally, in solution, it is possible to change the concentration of all the species at the same time by adding more solvent (or evaporating some solvent). If you dilute a solution by adding solvent, all of the concentrations will decrease. This will potentially change Q. If there are more species in solution that are products than reactants then Q will decrease. The reaction will then shift back towards the product side to reach equilibrium. If there are more species in solution that are reactants than products, then Q will increase upon dilution and the reaction will shift back towards the reactant side. When you dilute a reaction at equilibrium the reaction will shift in such a way to increase the total concentration (this means moving towards the side of the reaction with a greater number of species in solution). If you remove solvent, you concentrate the solution. Then the reaction will shift toward the side with the fewest number of species in solution.
A video on LeChatelier's Principle© 2013 mccord/vandenbout/labrake