What do the Jews teach is the purpose of the Sabbath? What do they do with all that free time?
Orthodox Jews teach that Shabbat is for the purpose of what many Christians call a "quiet time." That is, prayer and study of the word (esp. the Torah) are to dominate the day. The Jerusalem Talmud says, "The Sabbaths were given to Israel in order that they might study Torah" (Shab. 15:3.) What an excellent idea!
The eminent theologian Abraham Joshua Heschel wrote, "The Sabbath is not for the sake of the weekdays; the weekdays are for the sake of the Sabbath. It is not an interlude, but the climax of living" (The Sabbath, 14). He continues, "What was created on the seventh day? Tranquility, serenity, peace, and repose" (p.23). And later, "One must abstain from toil and strain on the seventh day, even strain in the service of God" (p.30). And finally, "Unless one learns how to relish the taste of Sabbath while still in this world, unless one is initiated in the appreciation of eternal life, one will be unable to enjoy the taste of eternity in the world to come. Sad is the lot of him who arrives inexperienced and when led to heaven has no power to perceive the beauty of the Sabbath..." (p.74).
In addition, many Jews make this quality family-time, even opening their homes to non-Jews.
Putting it all together, Shabbat is rest, yet not laziness. It is devotion to God, but not work. It is for study and prayer, but not a burden. And for those with families, a time to share.