To determine how the area of a square changes when its side length is increased by 25%, follow these steps:

1. Let the original side length be $s$.
- The original area of the square is:
$$\text{Original Area}=s^2$$

2. Increase the side length by 25%.
- The new side length becomes $1.25s$.

3. Calculate the new area with the increased side length:
$$\text{New Area}=(1.25s{)}^2=1.5625s^2$$

4. Find the increase in area:
- The increase in area is:
$$\text{Increase in Area}=1.5625s^2-s^2=0.5625s^2$$

5. Calculate the percentage increase in area:
$$\text{Percentage Increase}=\frac{0.5625s^2}{s^2}\times 100\mathrm{\%}=56.25\mathrm{\%}$$


The area of the square is increased by 56.25% when the side length is increased by 25%.

The correct answer is D. 56.25%.