Like Michael Quinion in today's World Wide Words, I'm surprised to learn that some people think the idiom grasp the nettle is a corruption of grasp the mettle. I suppose mettle isn't utterly fantastic here; if being on one's mettle means "ready for any challenge," I can see how grasp the mettle might be understood as something like "gird your loins" or "cowboy up." Still, it sounds odd if you've always been familiar with grasp the nettle.
The phrase is based on the folk wisdom that firmly seizing hold of a stinging nettle (or a nettlesome problem) is like yanking off a Band-Aid; doing it decisively lessens the pain. Quinion quotes an 18th-century verse that states the maxim (and even rhymes it with mettle):
Tender-handed stroke a nettle,
And it stings you, for your pains:
Grasp it like a man of mettle,
And it soft as silk remains.
Nice rhyme, and total hogwash, as I can painfully testify. Once upon a time, weeding along a backyard fence, I innocently grasped a nettle and pulled hard. It stung like crazy. According to the US Forest Service, the plant's poison is formic acid, and "contact with needle-like, stinging hairs on the twigs and lower surface of leaves of this plant can cause SEVERE SKIN IRRITATION AND MILD SKIN RASH." The all-caps emphasis is entirely appropriate.
Quinion wonders if the plant lore was a prankster's invention. I always figured the metaphor was coined by someone who had never been near a nettle -- possibly the same guy who thought "like taking candy from a baby" was a good way of saying "easy."