A landing party was a group of starship personnel equipped for missions involving landing on a planet's surface.
On 1947 Earth, while trying escape from the US armed forces, Nog claimed that Ferengi landing parties were to land in the United States of America. Captain Wainwright thought the first landing parties would invade Cleveland. (DS9: "Little Green Men")
The term was used by Starfleet as early as 2151, though the term "away team" was used as well. (ENT: "The Andorian Incident", "Fortunate Son")
In 2268, Captain James T. Kirk regarded landing party recommendations as a matter of judgment. M-5 chose its recommendations on the basis of logical selection. It did not choose Captain Kirk or Doctor McCoy on the basis that they were "non-essential personnel." (TOS: "The Ultimate Computer")
In 2338, the USS Tripoli sent down a landing party to the planet Omicron Theta. There they discovered Data and the remains of the destroyed Omicron Theta colony. (TNG: "Datalore")
By the 2360s, Starfleet adapted the term "away team" instead of "landing party," although it was occasionally used synonymously. (TNG: "The Last Outpost", "The Arsenal of Freedom", "The Royale")
Other cultures, such as the Ferengi, would still refer to the term "landing party" into the 2370s. (TNG: "Gambit, Part I"; DS9: "Little Green Men")
Landing party article at Memory Alpha, the canon Star Trek wiki.