A liaison officer was a person who represented the interests of their government to another.
From 2369 to 2375, Major (later Field Colonel) Kira Nerys acted as Bajoran Militia liaison officer to Deep Space 9, doubling as the installation's first officer under Benjamin Sisko. She succeeded Sisko as commanding officer after the former ascended into the Celestial Temple. (DS9: "Emissary", "What You Leave Behind")
In 2405 Lieutenant Junior Grade Kanril Eleya spent six months aboard Deep Space 9 as Starfleet's assistant liaison officer to the Bajoran Militia, due to the service being short on officers who spoke Bajoran and Cardăsda. She had actually applied for a post on the Klingon front, and remarked to her first officer Tesjha Phohl in 2409 that for all intents and purposes she'd been a glorified clerk. (Bait and Switch: Bait and Switch)
In 2410 Dal Kanril Eleya was assigned by Gul Kerim Morag to act as Klingon-Cardassian Alliance liaison to the USS Bajor, which had entered the mirror universe on a mission for Starfleet. (Bait and Switch: The Wrong Reflection)