"On the third new moon after the Israelites had gone out of the land of Egypt,.." -- Exodus 19:1
In Torah we read for the smallest detail.
The new moon represents new beginnings. This being the third new moon, it would have been about seven weeks since the Israelites left Egypt. So we think of the seventh day of creation, Shabbat! And what is different about this day? It is a day of rest, sure. But, it's not just a time to do whatever you want. Some people think that's what "sabbath rest" is, but that's not it. From here on in the Israelites will be defined by their relationship with God, and it's not a passive relationship like it's been in previous new moons. From now on they are a covenant people! It is impossible for the people of God to leave the covenant of God, but on Shabbat we enter more fully into our identity as covenant people: We read and study the texts that connect us with God, blessings are made and received. We screw up, sure... like the Israelites will, over and over. But, we are still people who are in a covenant with God. We are not passive. We are participants!