Eshet Chayil means "woman of worth," "valour" or "strength." The phrase comes from Proverbs 31:10, where it introduces a paean to her manifold virtues. "Who can find her," the author asks rhetorically. She rises while it's still night to bring food for her household, her lamp never goes out, her mouth is full of wisdom, and teachings of lovingkindness are on her tongue, and much, much more.
There is a widespread custom of singing Eshet Chayil on Friday nights at home before kiddush, as a song of praise to the woman of the house.
Lately some Jewish feminists have started to feel uncomfortable with the list of mostly domestic qualities enumerated in Eshet Chayil. Some omit the passage, some reinterpret it allegorically as a poem in praise of the Shechinah, the female presence of God, and some families add Psalm 15 in honour of the father of the house, for the sake of equality.
In religious circles you might describe as an Eshet Chayil a woman of exceptional virtue or stamina: "She gets up at 4am to make stuffed cabbage for 30 for Yomtov, packs her seven kids off to school, sits on umpteen committees and still has time to iron her husband's socks. What an Eshet Chayil!"
In fact, today, the Eshet Chayil is just as likely to get up at 4, make the stuffed cabbage, pack off the kids, then go to her job in the City, before coming back home and doing the socks.
Women's roles change, but the tradition's impulse to honour the Eshet Chayil remains.