For example, if I have 5 grams of X in 5 L of water. That would give me 1 g/L as the concentration. This yields a certain reaction rate.
Now, there are two possibilities:
A: grams increase, without an increase in volume.
or
B: grams increase, WITH an increase in volume.
So in case A, if I now have 10 grams of X in 5 L of water, that would give me 2 g/L as the concentration. Now as you know, an increase in concentration increases rate, which happens.
However, in the case of B, if I now have 10 grams of X but I also have 10 L of water, I still have 1 g/L. The grams of substance (or in otherwords, the quantity of reactants) increased, but the concentration stayed the same. In this situation, there would be NO increase in rate.