| Quote #1
I met a traveler from an antique land (1)
The very fact that the "land" is "antique" suggests that it is outdated, kind of like dial-up internet. The speaker implies that the traveler is coming from a place that is more primitive or older than the speaker's, a place that used to be home to a civilization and culture that has passed away.
| Quote #2
…Two vast and trunkless legs of stone
The statue is on its last legs; it has no torso, and the surrounding desert is doing its best to bury the "shatter'd" head. We are not told how the statue has come to be in this state, though we might infer that since it is located in an "antique land," perhaps it too has succumbed to the erosive force of time, like a lot of antiquities. This ancient object, too, is about to vanish; one can't help thinking that the legs will eventually suffer the same fate as the "shatter'd visage."
| Quote #3
Nothing beside remains; round the decay
Not only is most of the statue gone, but there isn't anything else around. The temples, palaces and whatever else might have adorned this landscape have all disappeared, leaving "nothing" but two legs and a head. "Decay" is an important word here; it implies that the statue has been slowly rotting or crumbling over a long period of time, and that it will eventually be completely destroyed or buried. It also suggests that the statue was once living, perhaps implying something about the status of art and its eventual fate.