It was capable of warping reality in nearby space and was influenced by the most rational potential. This means that it searched for parts of the universe that had become unstable in some way and rebuilt them along more rational line.
The first amaranth was created by maintenance engineers on Gallifrey to help counteract the warping effects caused by the black hole on the space time continuum. The Doctor possessed an amaranth. It contained an emergency function to transport its user to a more stable part of space. (PROSE: Christmas on a Rational Planet)