It was discovered by the Yeerks on one of Saturn's moons who after attacking it (unsuccessfully) with wave after wave of Hork-Bajir decided that it would be a useful weapon against the "Andalite bandits".
The Veleek could not be taken as a host so it was controlled by mutating it. The mutated form was attracted to morphing energy and would seek out and attack those it sensed morphing, even though it could not absorb this energy. It could only absorb energy from the Blade Ship's engines, and even then only what the Yeerks granted it, thus forcing it to serve them. The veleek's one weakness was water, which prevented the individual creatures from acting as one and apparently dissolved them. However, it also had problems with weight, being unable to carry Rachel while she was an elephant.
When dispatched against the Animorphs, the Veleek managed to capture Ax, but the remaining Animorphs swiftly realised that the Veleek had a key weakness; since it was drawn to morphing energy, all they had to do was keep morphing to keep it occupied, as it wouldn't continue to pursue a morphed target if another person was morphing nearby. Having learned of its weakness to water, the Animorphs defeated it by luring it out over the sea, Tobias carrying Cassie above the Veleek while in a cockroach morph, and Cassie subsequently morphing a humpback whale, thus causing the Veleek to fall into the ocean below.