The Vietnam War
Although the movie doesn't give an actual date for when any of its events are happening, it might be around November of 1969, since there's a newspaper with an article about the Manson trial lying around the boat, and that's when the trial happened. The war ended in 1975 with the fall of Saigon to the North Vietnamese.
Despite the beaches and sun, Vietnam wasn't actually a hot tourist destination in the 1960s and 1970s. The Vietnam War kind of ruined that for everyone. (Now you can go there and drink virgin piña coladas to your heart's content.)
In Apocalypse Now, Vietnam is all beaches and jungles—extremely hot, humid beaches and jungles. Everyone's bathed in sweat most of the time. We see peaceful rivers, lovely beaches, and beautiful palms gently swaying, all of which are either bombed, shot up, or strafed with napalm. We're witness to the slow, steady destruction of a beautiful country.
Much of the film takes place on the river, as Willard and crew pass army outposts, villages, groups of Viet Cong, and endless stretches of menacing jungle. By using the trip upriver to tie the action together, Coppola gives us a series of set pieces that could each be mini-films on their own. A set piece is described by screenwriter John August as "a scene or sequence with escalated stakes and production values, as appropriate to the genre […]. Done right, set pieces are moments you remember weeks after seeing a movie" (source).
Yeah, some of those scenes sure stick with you.
The movie makes the jungle feel like a nightmare or a fever dream. It's all so surreal: soldiers surfing in the middle of battle, Playboy Playmates escaping from crazed troops, a tiger suddenly leaping out of nowhere, Lance Johnson dropping LSD in the middle of a battle. The movie's trying to make the audience feel like the Vietnam War wasn't a conflict with real goals, just a senseless, crazy nightmare. The film evokes the feeling of what it must have been like to be there: chaotic, disjointed, nonsensical.