O, for a draught of vintage! that hath been Cool'd a long age in the deep-delved earth,
The speaker longs for a drink of wine or some other spirit that has been kept cool deep in the earth. "Vintage" wine is made from grapes from the same harvest, and people often refer to a particular year at a winery as a "vintage."
We have no explanation at this point for his sudden desire to get his drink on. He wants wine to just start bubbling up out of the ground, as if you could stick a tap right into the soil and let the good times flow.
Good wine needs to be kept cool, which is why people often store it in their cellars. According to Keats, the earth is like a giant wine cellar.
Tasting of Flora and the country green, Dance, and Provencal song, and sunburnt mirth!
Well, that makes sense. If you drink wine out of the earth, it's no surprise that it might taste like flowers ("Flora") and plants ("country green").
People sometimes jokingly say they want to "squeeze every last drop" out of the day, but the speaker seems to mean it literally.
Not only does the earth's wine taste like flowers, but it also tastes like dancing, song, and happiness ("sunburnt mirth"). Specifically, he is thinking of "Provencal," a region in the south of France known for its wine, sun, and a kind of poetic song known as "Troubadour poetry." Many Troubadours wrote poems addressed to an unattainable lover.
O for a beaker full of the warm South, Full of the true, the blushful Hippocrene,
The speaker wants to stick the south of France, or just the South in general, into a bottle ("beaker") and guzzle the whole thing down! He wants to distill the earth down to its powerful, intoxicating essence.
It's like when you go to the beach and wish you could just bottle the breezy ocean air to take back with you to school or the office.
"Hippocrene" is a reference that there is no reason you should know – Keats is showing off his knowledge of Greek mythology again.
Hippocrene is the "fountain of the Muses," a group of eight women (again, in Greek mythology) who inspire struggling poets. The fountain bubbles up out of the earth where Pegasus, the famous flying horse, is supposed to have dug his hoof into the ground.
He wants to drink something that will make him a great poet…and that'll get him drunk. The liquid from the Hippocrene is "blushful" because it is reddish, the color of both wine and a blush.
With beaded bubbles winking at the brim, And purple-stained mouth;
In delicious detail, the speaker describes the appearance of the wine. It has little bubbles at that burst, or "wink," at the brim of the beaker, like little eyes.
It also stains your mouth purple when you drink it, like any strong red wine will do.
That I might drink, and leave the world unseen, And with thee fade away into the forest dim:
What does all this talk about wine, inspiration, and drunkenness have to do with the nightingale? What happened to that old bird, anyhow?
The speaker sums up his intentions in these final two lines of the stanza.
He wants to get drunk on this magical wine so that he can leave the "world" without anyone noticing and just "fade" into the dark forest with the nightingale.
But isn't the forest part of the "world"? Apparently not. By "world" he might mean the world of human society, work, responsibility, and all that. The nightingale lives apart from this world.
Putting aside all this business about Provencal and Hippocrene, the speaker wants to drink for the same reason many people drink: to forget his problems for a while and to have a more carefree state of mind.