(covers information from several alternate timelines)
Nakan memorial
A monument was an object set aside as a memorial to an event or person. Scanning for monuments was a way to discover if a planet had previously hosted a civilization. (TNG: "The Chase")
Monuments did not need to be physical objects, and the term could even be used abstractly. For example, a race of Ancient humanoids engineered humanoids to be a dominant life form as a monument to their existence. Gosheven described the colony on Tau Cygna V as a monument to everyone who had lived there. (TNG: "The Chase", "The Ensigns of Command").
In an alternate reality, Nelson's Column, a monument honoring Horatio Nelson existed in London. (Star Trek Into Darkness)
More informally, in 2372 Julian Bashir described the state of Miles O'Brien's quarters as a monument to his year as a bachelor. Similarly, in 2375, Ezri Dax, through her former personality Joran Dax, snarked that the crew quarters of Greta Vanderweg as a monument to bad taste. (DS9: "Accession", "Field of Fire").
Tom Paris once described his Paris Program Alpha-1 holoprogram as a monument to hundreds of hours he should have spent with B'Elanna Torres. (VOY: "Vis à Vis")
Figuratively, the term "monumental" could be used to describe particularly large works, or moments of particular historic significance. On Kataan, the construction of atmospheric condensers was considered a monumental task, and therefore unfeasible. (TNG: "The Inner Light") crewman Daniels described the Battle of Procyon V as a monumental moment in history. (ENT: "Azati Prime")
Specific monuments
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On a Delta Quadrant planet inhabited Humans transplanted by Briori, a cryostasis chamber containing the 37's had become regarded as a monument. (VOY: "The 37's")
The Delta Quadrant planet Tarakis contained a monument to the Nakan massacre. (VOY: "Memorial")
By the 24th century, the whole area of the settlement where Zefram Cochrane originally built the Phoenix had become a national monument. (Star Trek: First Contact)
Gul Darhe'el was buried under one of the largest monuments on Cardassia Prime, a fact which Gul Dukat witnessed and offered as proof that Darhe'el was indeed dead when Aamin Marritza claimed to be him, alive and well. (DS9: "Duet")
After arranging for the Cardassian Union to join the Dominion in 2373, a monument to Gul Dukat was erected outside the gate to the Imperial Plaza on Cardassia Prime. (DS9: "By Inferno's Light")
In the 31st century, or at least the version of it from which crewman Daniels originated, Earth hosted a monument to the United Federation of Planets. The monument disappeared in a version of this future in which due to the Temporal Cold War the Federation did not exist. (ENT: "Shockwave, Part II")
