Rashi explains: One should ensure that his requirement of having pleasure on Shabbos should not be disturbed because of the prohibition of eating tevel (produce which has not been tithed yet). Take precautionary measures to remove the prohibition in order that the produce can be consumed and enjoyed.
Rabbi Yosef Lieberman in his sefer, Mishnas Yosef comments that this verse is also teaching us how one has to have a fear of Hashem on Shabbos and Yom Tov, even more than he does during the weekdays, for the laws of Shabbos are like mountains hanging on a hair, for they have few Scriptural allusions, but many halachos. It is extremely easy to stumble and transgress one of the many prohibitions on Shabbos.
Furthermore, he writes that these are days of pleasure and enjoyment; a time that is vulnerable for sin, like the Tur (O”C 529) writes. One should sit on Shabbos with a tremendous trepidation so that he does not inadvertently sin on Shabbos. And one who attempts to purify himself, Hashem will assist him.
The Gemora says elsewhere that one does not need to be concerned about eating d’mai (produce purchased from an am ha’aretz, and we are uncertain if ma’aser was taken from it) on Shabbos because we can ask the am ha’aretz, and we are confident that he will not lie on Shabbos.
I once heard from Rav Shmuel Feivelson the following explanation: Shabbos is a sampling of the World to Come. We are basking in the presence of the Shechinah. It is impossible to lie when the truth is staring you straight in the face.