The way we see it, the first word of the title gives us our topic and the second word gives us the mood. "Immigrant" tells us that this poem is going to tackle the immigrant experience one way or another. And then "Blues" tunes us in to the feeling of sadness or melancholy weaved throughout. It lets us know that the poem might be something of a lament, or at least will address some of the hardships an immigrant faces. Quite literally, our speaker is an immigrant, and he's totally down in the dumps.
Of course, "Blues" has another layer of meaning, too. "Blues" is also, as you probably know, a genre of music (which just so happened to be the foundation for rock and roll). Blues, as a music form, traditionally has a lot of repetition in its lyrics, and this association gets us ready for the way this poem is going to keep repeating variations on a name for the immigrant experience.
So all in all, it's a pretty nifty title, right? It tells us exactly what we're dealing with, and clues us in to how to read the poem. Think of it as a blues song about some very serious stuff, but don't forget to enjoy the melody, too.