An EPS conduit was a part of a starships propulsion systems. The conduit would take small amounts of plasma from the warp core or impulse engines and redirect it throughout the ship for use in powering other systems.
History and specifications
Following a battle with two Cardassian Galor-class warships in late 2373, the EPS conduits on deck seventeen of the USS Enterprise-E suffered significant damage and were in need of immediate repair. (TNG - The Dominion War novel: Behind Enemy Lines)