Now for the happy ending. The sound of your voice reading a favorite, simple poem fills the sad gloomy night with music. Yay!
And the cares that infest the day,
The speaker reminds us one more time of how tough the day has been. The night has beautiful music, but the day is "infested" with worries and problems ("cares").
When we hear the word infested, we think of rats and roaches and nasty crawling things. That imagery makes this last image of daytime even more intense, and emphasizes the contrast with the beautiful, musical, poetry-filled night.
Shall fold their tents, like the Arabs, And as silently steal away.
Now all of those nasty, rat-like cares that infested the day are going away. Longfellow pictures those cares being like "the Arabs" folding up their tents.
At first glance, that might sound a little weird, and maybe not so PC, but we don't think Longfellow means it like that. We think he wants to call up an image of the quiet and calm of the desert, and a silent people who come and go without a sound. He wants a soothing image of how troubles can vanish without a trace.
In the end, this poem (especially in its last lines) is meant to do exactly what the speaker says good poems should. It's supposed to make you feel better about the world, to smooth away the things that have been worrying you and leave you completely at peace.