(covers information from several alternate timelines)
A conduit is a medium to transfer energy between two points. They are often built into walls of habitat areas.
When Geordi La Forge and Ro Laren cut a micro-hole into the bulkhead above Ten Forward, he was concerned about hitting conduit 227, but he managed to get by without rupturing the conduit. (TNG: "Power Play")
On Cardassian space stations, conduits are accompanied by Jefferies tube-like crawlspaces, which run throughout the station. These crawl spaces are lined with duranium alloy, which prevents them from being scanned by sensors. This once allowed Major Kira Nerys to fool a Cardassian warship into thinking Deep Space 9 had 5,000 photon torpedoes when in fact it only had six. (DS9: "Emissary") It also allowed a group of Starfleet officers to hide from the Bajoran Militia during a siege of the station in an attempted coup d'etat by the Alliance for Global Unity. (DS9: "The Siege")
Miles O'Brien and Benjamin Sisko once crawled their way through a conduit to disable the self-destruct program that threatened the station as part of the counter-insurgency program they had accidentally activated. (DS9: "Civil Defense")
While trapped inside his mind, which he visualized as DS9, Julian Bashir attempted to use the conduits to reach Ops. However, the telepathic attack he had suffered caused him to continually re-emerge on the Promenade. (DS9: "Distant Voices")
Quark once decided to assemble an all-Ferengi team to rescue his mother Ishka from the Dominion. He had to find his brother Rom, who was on duty at the time and working in one of the station's conduits. After informing Rom of the situation, Quark got lost and found upon opening the hatch at the end of a conduit that he had reached Captain Sisko's office. (DS9: "The Magnificent Ferengi")
In an alternate timeline in 2371, the USS Voyager encountered a planet that had been devastated by a polaric ion explosion. Kathryn Janeway was assured by Pe'Nar Makull that nothing would go wrong in the polaric radiation plant unless she fired a weapon near a polaric conduit. These conduits were exposed and ran lengthwise down the corridors of the plant. (VOY: "Time and Again")