Diminishing returns

Imagine adding defects to a perfectly ordered crystal, the first defects added will increase entropy much more than the others:

Likewise, increasing temperature near absolute 0 will increase entropy much more than increasing the temperature of a hot object:

One analogy I've seen used is that shouting in a silent room of people produces more disorder than shouting into a room full of people talking. Actual explanations are given by statistical arguments.

For a really simple example, picture a 4-atom crystal and assume a defect means a missing atom. One defect means 4 microstates, two defects means 6 microstates, the first defect is therefore more significant.