To increase the rate of a reaction, why would you increase the concentration of the reactants?

If you meant a Irreversible reaction Explanation :

You can increase reactant rate of a closed system I.e. Closed container by increasing reactant concentration by injecting it or adding it in the container. The increase will cause more reactant particles to collide per unit volume and the proportion of fruitful or successful collisions will increase (refer to collision theory) Therefore, Increaing rate of the reaction

If you meant a reversible reaction Explanation :

Increasing the concentration of reactants in a dynamic system(reversible chemical reaction) would mean that the equilibrium position will shift to the right
(Li Chêtliers Principle- if stress is applied to the system it will partially oppose the change) meaning initially the rate Of forward reaction will increase initially and than slowly decrease till equilibrium is re-established.

Additional info:
You can increase rate of reaction by:
1) Altering Surface area of a solid reactant.
2) Alteing Temperature (depends on Endothermic/Exothermic reactions)
3) Adding a catalyst
4) Increaing Concentration( For gaseous reaction altering pressure or volume )