What happens in an aqueous solution as the concentration of H3O+ decreases?

Each water molecule can form four hydrogen bonds with other water molecules due to its polar nature.
Therefore, a hydrogen atom taking part in a hydrogen bond between two water molecules can shift from one water molecule to the other. When this occurs, it leaves its electron behind. Therefore, the hydrogen ion will be a proton written as H+. The molecule that has lost its proton is called a hydroxide ion with the symbol OH-. The molecule that has accepted the extra proton is now called H30+ and is known as a hydronium ion. It is sometimes written as simply H+.
The process described above is dissociation of water molecules. However, these molecules can re-form water exists in a state of equilibrium with a neutral pH of 7.
Anytime a substance increases the H+ ion concentration in solution, it is called an acid. A base reduces the H+ ion concentration of a solution. Water is technically both an acid and a base. A shift in the number of H+ ions where they outnumbered the OH- ions would result in a lowered pH and the solution would be acidic. A shift in the number of H+ ions where they were less than the OH- ions would result in an increase in pH.
In a water- based solution at 25 degrees C, the product of H+ ions and OH- ions = 10 -14. Basically, in a neutral solution, there is an equal number of H+ and OH- ions.
The pH of a solution = -log (H+) therefore, in neutral water, the H ion concentration is 10-7 and if one uses the formula above, pH= - (-7)= 7. 
The pH scale is written from 1 to 14. Neutral water has a pH of 7 and values below 7 are increasingly stronger acids. Values above 7 and continuing to 14 are increasingly stronger bases.
In a solution, if the number of H30+ ions (also written as H+ ions) decreases, the pH of the solution will increase. There will be a shift toward more OH- negative ions as the H3O + ions decrease. 
 
 
https://www.sciencebuddies.org/science-fair-projects/references/acids-bases-the-ph-scale

H3O+ is called the hydronium ion in the aqueous solution. The variation of H3O+ in an aqueous solution affects the acidity of the said solution. Water molecules can dissociate into H3O+ and OH- at a given temperature. For example, at 25 degrees Celsius, H2O dissociates into:
2 H_2O = H_3 O^(+) + OH^(-)
With
K_w = [H_3 O^(+)] [OH^(-)]
Where:
[H_3 O^(+)]= Concentration of hydronium.
[OH^(-)]=Concentration of hydroxide.
Kw = 1.00x10^(-14), (Constant). 
Changes in the concentration of H3O+ in the solution are affected by the temperature and the species that is dissolved in water. 
Acidity is measured by the concentration of H3O+. It is represented as:
pH = -log [H_3 O^(+)] .
As the concentration of H3O+ decreases, pH increases. In other words, as the concentration of H3O+ decreases, the solution becomes less acidic.
In a neutral aqueous solution (pH = 7), there is roughly equal populations of H3O+ and OH-. Changing the pH or acidity of the solution can also mean changing the concentrations of H3O+ and OH-. 
 

H3O+ represents an acid.
As you might have guessed, H3O+ is nothing but H2O + H+
(H+ is a free positive ion, and in aqueous solution is will be coordinated by the H2O molecules, and hence H+ exists as H3O+)
H2O + H+ = H3O+
So, decreasing the H3O+ concentration implies a decrease in H+ concentration. So acidity of the solution decreases. Note: pH is a measure of the acidity of the solution. pH = - log [H3O+].
Thus, as H3O+ concentration decreases, pH increases.