Our speaker embarks on a rather epic journey: he plans to offer us three variations on a traditional elegy, all of which commemorate the life and work of the poet William Butler Yeats (the W.B. Yeats of the title). Things start off simply enough: the speaker imagines what it must have been like for Yeats on the last day of his life, and the speaker begins the difficult process of imaging a world in which Yeats's poems will still exist even though their author is gone.
Abruptly, the tone of the poem shifts. Suddenly our speaker is addressing Yeats himself, chiding him for all of his mistakes, but also admiring Yeats's poetry.
Finally, the poem lapses into an oh-so-traditional elegiac form. This doesn't last for long, though – soon the speaker is off and running again, thinking about the problems of the here and now. It's 1939 and the world is on the brink of war (World War II, to be exact). In other words, things aren't so happy right now, and the speaker isn't silly enough to think that poetry can bring world peace. But that doesn't mean he thinks poetry isn't valuable. In fact, it's all the more valuable in desperate times, as Yeats's work demonstrates.