Every 7th year and every 50th year were supposed to be special in Israel. Just like there were Sabbath days of rest, there were also Sabbath years of rest. The fields and vineyards were supposed to be allowed to lie fallow every 7th year. And, slaves and lands were to be freed every 50th year. That 50th year was called the Jubilee (a year of joyful sounds; a year for joyful music). During the year of Jubilee slaves were to be given their freedom and lands were to be returned to the family that originally owned them.
To me, the most intriguing thing about God's word to Israel in this passage is the timing of God's supply. You would think that if God promised to bless every 5th year's harvest enough to make it last until the 3th year (which He did), then the people would have had no problem observing the 7th year rest. But actually, they did struggle to believe God for this. The proof of their disobedience is found by comparing the promise and the record (Leviticus 26:34-35, II Chronicles 36:17, 20 and 21 and Jeremiah 25:9-12). God warned the Jews that if they didn't observe the Sabbath years; if they failed to let the land rest, then He would have to rip them from the land. It would certainly rest without them there to inhabit it! And, that is exactly what ended up happening. The land eventually rested (most specifically) while the Jews were in Babylon.