All of the yomim Tovim are referred to in the Torah as "mikraei kodesh." This term is so fundamental that we incorporate it into our tefillah and Kiddush on yom tov. There are different interpretations as to precisely what mikra kodesh requires of us. Rashi (Vayikra 23:35) quotes Toras Kohanim that understands "mikra kodesh" as the source for treating yom tov as unique in a variety of ways. Special food and drink, clean clothing, and yom tov davening are all fulfillments of declaring the day as a mikrah kodesh. The Ramban (Vayikra 23:2) interprets "mikra kodesh" as referring public gatherings for matters of kedusha; public tefillah and Hallel on yom tov are elevated to the status of mitzvos min haTorah as practical fulfillments of "mikra kodesh."
In contrast to Rashi and the Ramban who interpret "mikra kodesh" as a requirement of positive action, Tosfos (Shevuos 13a) quote Rabbeinu Tam who equates "mikra kodesh" with refraining from melacha. The basic prohibition of melacha on yom tov is already mentioned explicitly. The additional dimension of "mikra kodesh" teaches us the mindset we must attain as we refrain from melacha. One who does not perform melacha on yom tov because he is lazy, and not specifically for the purpose of sanctifying the day, does not violate the prohibition of doing melacha but also does not fulfill the mitzvah of "mikra kodesh."
Rav Soloveitchik zt"l expanded on this interpretation of Rabbeinu Tam that a person's motive for refraining from melacha is essential. Chazal (Berachos 20b) teach us that women are obligated to recite Kiddush on Shabbos according to the Torah. Notwithstanding Kiddush being a time bound positive mitzvah from which women are usually exempt, there is a halachic connection between Kiddush and the prohibition of melacha, in that whoever is forbidden to do melacha on Shabbos is obligated to recite Kiddush. This halacha is derived from the tradition that the terms "Shamor" and "Zachor" used in the Torah concerning Shabbos were recited simultaneously by Hashem. "Shamor" refers to the prohibition of melacha where "Zachor" is the source for the positive obligation to recite Kiddush. The connection between Kiddush and melacha is not only a technical one concerning who is obligated to perform the mitzvah of Kiddush. Kiddush is linked to melacha because the purpose of Kiddush is to make a verbal declaration why we are refraining from melacha. Rather than merely taking a day off from work, we begin Shabbos with an affirmation, through our recitation of Kiddush, that Shabbos is a mikra kodesh. As such, refraining from melacha on both Shabbos and yom tov is only complete if accompanied by Kiddush.
There is a second role that Kiddush plays on Shabbos and yom tov. Chazal (Pesachim 101a) teach us that Kiddush must be recited in the place one eats. The connection between Kiddush and seuda is similar to the link between Kiddush and melacha. As Rashi quoted from Toras Kohanim, one must eat and drink on Shabbos and yom tov in a manner that is consistent with mikra kodesh. Merely eating a special meal does not necessarily fulfill this obligation; the intention to eat as a way of sanctifying Shabbos and yom tov is necessary, and Kiddush is the verbalization of our intention. Eating a meal not preceded by Kiddush is as deficient as refraining from melacha without reciting Kiddush.
Kiddush enables us to properly observe mikra kodesh in its multiple dimensions. As we refrain from melacha and partake of our seuda within the context created by Kiddush, our actions become a fulfillment of mikra kodesh.