We say in Lecha Doidi that Shabbos is "soif b'ma'aseh, b'machshovo tchilo" — last in action (creation), first in thought.
The simple meaning is that Shabbos was the last day of creation, but it was first in thought of Hashem — the whole creation was for its purpose, and it was the culmination of creation. Just like the times of Moshiach.
But if you learn Kabbala and Chassidus, they look at this statement literally (as oftentimes happens, the "esoteric" interpretation of a statement according to Chassidus is more literal than pshat, the supposedly literal interpretation).
Kabbala talks of a concept of "Shabbos before the first Sunday" — that before the world's creation started on the First Day (Sunday), there was a Shabbos. But this was not really Shabbos as a part of creation. Creation happens through the mode of "speech", which (as Ramban and many others explain) means that Hashem creates something (as if) outside of Himself — just like our thoughts become speech only when they are outside of ourselves in some other medium than our mind and reach another person (or are supposed to reach, have a potential of reaching; so, even if I write my thought in a notebook and hide it, it may be poor communication, but it is still "speech"). On the other hand, the "Shabbos before Sunday" was in Hashem's thought: it was Hashem's design of the world that was still one with Hashem before Hashem started implementing the design into "reality".
So, literally, in the realm of creation, Shabbos was last (sof b'ma'aseh), but first, before that, it already happened in the realm of thought (b'machshava tchilo) preceding the speech.
The thing is: the first "official" Shabbos, the one following the first week of Creation, was also in thought. This is the meaning that Hashem "ceased creating" on Shabbos. It doesn't mean that He literally stopped bringing the world into existence yesh m'ayin — the world would not exist then. As we learn from Chassidus (although this idea existed before Ba'al Shem Tov), creation is happening every moment, yesh m'ayin, ex nihilo. And it happens through the same "speech", the same "words" that were used to create the world ("Forever, oh G-d, are your words in Heaven" — again a case of Chassidus doing super-literal interpretation and explaining that the words "Let there be separation..." that created the Heaven are still literally in Heaven, being spoken every moment and giving it existence).
But, on Shabbos, Hashem stopped "speaking". After a week of creating the world through "speech", as something outside of Himself, Hashem retracted the world back into His Mind (so to speak). And that is what Shabbos is: being inside Hashem's Mind, since the same process repeats itself every week. That is why it is the holiest day — it is holy not because of some contract we made with Hashem that sanctified this day, but because on it we are literally inside kedusha, inside Hashem, so to speak.
The meditation on the above, at length, both during davening on Shabbos, and during the rest of activities, should give a person a special feeling of both love and awe for this day.
And now I refer you to the post by Rabbi Oliver: "Shabbos is not a day of rest".