This is the first use of the English word "Sabbath" in the Bible. This usage comes from the Hebrew word shabbath (Strong's 7676). The word shabbath comes from a primitive root word shabath (Strongs 7673) which is translated in various places "cease," "rest," "away," "fail," "celebrate," and miscellaneous other words, some of which precede this usage of the word shabbath. For example, Genesis 8:22 uses "cease," and both Genesis 2:2-3 and Exodus 5:5 use "rest."
Moses was transmitting to the Israelites a Sabbath commandment from God, four chapters before their arrival at Sinai where the tablets of stone (the Ten Commandments) were given. There is no indication that this Sabbath commandment was something that was newly initiated by God at this time. In fact, other verses state that the Sabbath Day of rest was initiated at creation (see Genesis 2:2-3; Exodus 20:11). God said through Moses, "Tomorrow is a day of solemn rest...". He did not say, "This is a new command: from now on, every seventh day is to be a solemn rest, etc."
This appears to be a reminder to the Israelites of God's Sabbath requirements, and specifically with regard to the collection and preparation of manna. It must be remembered that the Israelites had been in captivity for hundreds of years, and that they had not, during those years, enjoyed the freedom to obey God's Sabbath commands (see Exodus 5:1-5). Now that they were free from Egypt and the restrictions of slavery, they needed to be reminded of their obligations as the children of God. This verse reiterates that the seventh day was set apart by God to be holy.
The Israelites were commanded to rest solemnly. This does not mean that they were to be miserable, but that they were to be strict in their keeping of this period of rest. Even their food preparation was used as an example of God's intent: Other verses show that they were to collect twice as much manna on the previous day. This verse states that they were to do any preparation and cooking of the manna on the previous day. Any leftover, unprepared manna could be left unconsumed until the Sabbath without fear of it rotting (as it did on the other six days of the week). This was a miracle, which proved to the Israelites on a weekly basis that God continued to put His blessing on the Sabbath day. It also clearly revealed to them, after hundreds of years of slavery, which day was God's Sabbath.