Batten down the hatches and hang on to your umbrellas. The "Gale" here represents the kind of winds of misfortune that can blow into our lives. And yet, argues the speaker, that's the time when hope is the most precious to us.
And sore must be the storm - That could abash the little Bird (6-7)
Hope is the bees—scratch that, the bird's—knees, but there are times when even hope can fade. Sure, it takes an awful occurrence for that to happen ("sore must be the storm"), but that kind of suffering can throw hope off its game.
I've heard it in the chillest land - And on the strangest Sea – (9-10)
Cold lands, strange seas—these aren't your typical tourist destinations. The speaker is recalling times where her suffering made her feel as if she was transported to these awful places. Luckily for her, hope was along for the ride.
Yet - never - in Extremity, (11)
Extremity might sound like the next generation of BMX and skateboarding sports, but here it's just another word for suffering. Our speaker goes on to describe how, even in her extreme moments of awfulness, hope was good enough not to charge for its services… which we think is nice. It sure helps make all the terrible suffering more bearable.