The poem is set in Ireland (probably the city of Dublin) sometime after the Easter Uprising of 1916. For those of us who don't know what the Uprising was, here's a quick rundown.
At the beginning of the 20th century, Ireland was ruled by the English. The Irish were never big fans of that, but things looked like they were going to get better when the English promised to hand Ireland back to the Irish people in 1914. The problem is that this is the same year World War I broke out. The English needed all the territory and military fighters they could get, so they broke their promise and told the Irish they'd get their country back after the war was over. You know, after a few hundred thousand Irish people had died fighting for the English army.
Well as you can imagine, the Irish people didn't take kindly to that. And after two years into the war (1916), there was no end in sight to the conflict. So during the Easter week of 1916, some Irish patriots got themselves some guns and pitchforks and seized control of the country. Now you might think that England would be all like, "Yeah, fair enough." But instead they devoted a bunch of their military forces to crushing the Irish Uprising. By the time the whole thing was over, 300 people were dead and 17 more were sentenced to be executed for helping to plan the rebellion. So yeah, that's the kind of Ireland that Yeats is talking to in this poem.
At the start of this poem, it seems like everything is good and hunky-dory in the Land of Eire. The speaker (probably Yeats himself) gets to walk down the streets at the close of day and exchange "polite meaningless words" (6) with the common folk of Dublin. But in stanza 2, Yeats starts talking about some of the people who have died in the Easter Uprising, and things get a little more real on us.
In the third stanza, we suddenly find ourselves staring at some sort of "living stream," probably somewhere out in the Irish countryside. But it turns out that this is just a metaphorical place where the dead Irish fighters will live on forever like a stone. At the end of the day, we return back to the streets of Dublin, which are a little emptier now that over 300 people are dead.