Stanza 9 Summary

Get out the microscope, because we’re going through this poem line-by-line.

Such songs have power to quiet
The restless pulse of care,

Here's where Longfellow, through his speaker, makes his pitch for this particular kind of honest, humble, heartfelt poem. He calls them "songs," which might make us think of lullabies or folksongs or other kinds of down-home melodies.
He also tells us that they are powerful, that they can calm down ("quiet") the "restless pulse of care."
We like that phrase. We think it's a really good description of how the speaker is feeling, as if his "care" (that means worry or unhappiness) was making his heartbeat uneven and jumpy. These poems are supposed to smooth everything out and make it OK.

And come like the benediction
That follows after prayer.

Here's another image of what a good, honest poem can do. It works like a blessing (a "benediction") after a prayer.
Blessings from priests or from God, are definitely meant to be comforting, to turn your worries, your prayers into satisfaction and happiness.