what does sabbath mean?

been pondering about this as i see my colleagues observing it. there are families at school who don't quite do so.. but there are some who say that homework cannot be done on that day - it is a rest day. what does it mean to rest? the other part of it probably involves rest "to the Lord". how much of the OT and its law apply to after Jesus' time? we have been redeemed and we no longer live under the bondage of the law. i will be thinking more of it as the next big holiday approaches... but maybe i wont, given that more family will be here in two weeks.