God told Ezekiel about the people of Israel: I gave them my statutes and showed them my ordinances, by whose observance everyone shall live. Moreover I gave them my sabbaths, as a sign between me and them, so that they might know that I the LORD sanctify them (Ezek 20.11-2).
God's commandments lead to life; a life lived in obedience to them is a truly human, prosperous, flourishing life. It is one thing to be alive from a purely biological point of view, and it is another to feel "alive" in a fuller, deeper way. The depressed are alive in the first sense but not in the second; the happy and joyful are alive in both ways. The lesson here is that God's commandments lead to life of this second sort: they lead to eudaimonia, to use the Greek philosophical term.
But because we are sinful and weak in various ways, it is very difficult for us to keep God's commandments. Through our disordered desires and ignorant prioritization of temporary, transient pleasures over lasting goods, we sabotage ourselves in the quest for a life well-lived. Therefore God commands the sabbath as a reminder that I the LORD sanctify them (v. 12). We don't sanctify ourselves, though we make efforts towards sanctification, so much as God sanctifies us.
When we sabbath, we rest from our labors. Rest is important because it is the way we are made stronger. You can't get much stronger lifting weights every day; you will exhaust yourself and do more damage than good. You need periods of rest, so that your body can rebuild itself stronger than before. I imagine that in the same way, our spirits need rest as well. We need a day of rest, in which we remind ourselves that we depend upon God, not our own strengths, and in which we bring supplications and prayers before him, asking him to renew us for another week of struggle and toil.
I am not particularly good at keeping Sabbath, which is perhaps why I am not particularly good in general. Holy Week provides ample opportunities for reflection upon God's grace and providence, however, as we consider Christ's sufferings, death, and resurrection. The ultimate Sabbath is Easter Sunday, when, confronted with the resurrection of Christ, we receive the greatest encouragement and empowerment of all: as Luther said, God in Christ has defeated death, sin, the law, the devil, evil, and everything else that stands in our way, and this victory he shares with us when we ask for it.