The term ultraluminous infrared galaxy (ULIRG) indicates a galaxy emitting more than 1012 times solar luminosity (LSun) in the far infrared. Such a galaxy also falls under the term luminous infrared galaxy (more than 1011 times LSun in far infrared) and potentially under the term hyperluminous infrared galaxy (more then 1013 times LSun in far infrared). (Sources also cite these thresholds as applying to the galaxy's full bolometric luminosity, sometimes stipulating that most of its emission is within the infrared or far infrared; I presume this is the typical case for such bright galaxies.)
A LIRG is often a starburst galaxy and/or has an active galactic nucleus. The infrared would be from black-body radiation at a much lower temperature than stars themselves, i.e., of clouds heated by the young stars the galaxy is creating, and if the clouds are dusty, the infrared may be the only observable sign of star formation. A ULIRG is typically a nearby galaxy (low redshift), and often the result of a merger. When distant, it is a useful sign of star formation.