One of the Mitzvos discussed in this week's Parsha is the counting of the Omer. The Posuk says that we are to begin this count during the holiday of Pesach "ממחרת השבת," "on the day after Shabbos" (ויקרא כ"ג:ט"ו). The next Posuk says that this count ends on the day following the seventh Shabbos (שם פסוק ט"ז). The question of what is meant by the term "Shabbos" in these Pesukim was the subject of a great debate. The Tzeddukim, the Sadducees, who rejected the Oral Torah, held that Shabbos means the Sabbath, that is, Saturday, as it usually means. The problem is that there would appear to be no reason to begin counting the Omer on the day after Shabbos (Sabbath) because nothing significant happened on or after the Shabbos during Pesach. The Rabbanan therefore explain that the term "Shabbos" in these Pesukim in fact refers to Yom Tov. The count must therefore begin on the day following the first Yom Tov day of Pesach, which makes sense, because this was the day on which the Jews became a free nation and could look ahead to better things.
The only question is why the Torah uses the word "Shabbos" to signify the first Yom Tov day of Pesach. Perhaps one could suggest that the fact that Hashem passed over the Jewish homes in Egypt when slaughtering the Egyptian first-borns represented the first act where Hashem treated the Jewish people with a special holiness, highlighting the notion that they were holy, or separate, from their Egyptian neighbors. Consequently, the Torah refers to the day on which all this happened as Shabbos, because that day signifies the height of holiness. Similarly, reference is made to Shabbos in connection with the conclusion of the Omer count because that count ends with Shavuos which is when the holiness of the Jewish people became complete with their acceptance of the Torah. Therefore, once again, the term Shabbos is used to highlight the special holiness of that day. The term Shabbos thus hints to us the extra holiness of these two special days.