Why is the base of a building made wider?

Ignoring practical justifications such as the desire to fit everything needed into the ground floor then the two primary reasons which spring to mind are:

1. Pressure.

Pressure = force / area. So, just as by spreading yourself out you might be able to cross a frozen lake without the ice breaking (where standing on tip toes to do this would be a bad idea) the same applies here. If the base of the building was very narrow then the weight of the building would put an increased pressure on both the lower structure and the earth underneath. If the lower structure of the building was strong enough to support this then the foundations may not be. It is simply a case here of spreading the load out to reduce the risk of collapse or subsiding.

and

2. Stability

A wider base provides a more stable platform on which to build. Consider how a thick tree will bend less in the wind than a thin one. Naturally engineers like to build stable things when possible and a narrow base would increase the risk of the building falling over!