Why is grass so important to people?

Grass has a few benefits. The obvious one is that it tends to look nice - if properly cared for. It also is much softer underfoot than bare ground. Another reason for grass is that it can hold soil in place.

In areas where grass is not viable, other approaches are taken. In dry areas like, say, Phoenix, Arizona, yards are often covered with gravel instead of grass. Since there is so little rain, there is much less worry about keeping soil in place and the gravel is sufficient for the purpose. In areas that are heavily forested, grass doesn't get enough sunlight to thrive so the ground becomes covered with leaf or needle detritus that absorbs much of the moisture and provides some protection from runoff. Other areas will be covered with moss, which performs much the same ecological purpose as grass.