Gen. 1:5:
וַיְהִי עֶרֶב וַיְהִי בֹקֶר יוֹם אֶחָד
And it was evening, and it was morning, one day
Gen. 1:8:
וַיְהִי עֶרֶב וַיְהִי בֹקֶר יוֹם שֵׁנִי
and it was evening, and it was morning, a second day.
Rashi says it is "the day of the One". Because the angels weren't created until day two, God was the only sentient being on this day. Obviously this reason doesn't apply from day two onwards, per Rashi's words.
Kli Yakar prefers to say that the verse is asserting that one God created both light/day, and dark/evening, as the Sages would take care to mention one alongside the other. This was so that heretics would not conclude that some other entity created darkness and night when confronted with two opposite states stemming from one creative act.
Ramban, (in addition to what he says in user6591's answer), says that this day was actually one day, as opposed to the fourth day, when the existence of the sun caused there to be 'many' days and nights, in a 24-hour period, depending on location on the earth, and the earth's rotation.
I remember seeing that rishon, what you are calling an ordinal number, is only in reference to something else, i.e. the day before or the day after, neither of which existed. Therefore echad was used. This is said by the Ramban.
Except for the Baby Seal's excellent answer, I remember one more explanation.
In Judaism the day starts from the evening. For example, Shabbath starts on Friday evening and finishes on Saturday evening.
This rule is learned from this very verse you are talking about. You can interpret "one day" as "the same day", meaning that evening and morning belongs to the same day.
- And God called the light day, and the darkness He called night, and it was evening and it was morning, one day.
ה. וַיִּקְרָא אֱלֹהִים | לָאוֹר יוֹם וְלַחשֶׁךְ קָרָא לָיְלָה וַיְהִי עֶרֶב וַיְהִי בֹקֶר יוֹם אֶחָד:
- And God called the expanse Heaven, and it was evening, and it was morning, a second day.
ח. וַיִּקְרָא אֱלֹהִים לָרָקִיעַ שָׁמָיִם וַיְהִי עֶרֶב וַיְהִי בֹקֶר יוֹם שֵׁנִי:
I discuss some of the logical reasoning in Breishis - Creationism and Evolutionism
Logically, we can consider Creation in a way like building a computer program from modules. Each "day" is a different module turned on and off for the unit testing. This is why the first time, when time is created, is יום אחד (one day) and the following days are of the form "a second day". It is only on "the sixth day" and the finish (ויכולו) that the actual execution begins. As a result, nothing before the beginning of man and civilization (Adam) needs to be mentioned.
The fact is that with the initial creation of space and time, a day was created. Once that was done and a second dark/light cycle created, it was a second day. Something that somewhat duplicated the existence of a cycle a second, third, fourth, and fifth time. It was only with the creation of "the sixth day" that the universe reached the point of being able to continue "according to the laws of nature" and had enough parts in existence to be able to continue to exist. However, it was only with the creation of "rest" that the "program" actually began running.
Note that the third day was the "plant module" and the fourth day was the "sun moon and stars module". This implies that the light of the stars was created reaching the Earth no matter how far away the stars were. These "modules" could not run independantly.
Note that this also answers how vegetation could be created "before" the sun. It also answers why dinosaurs do not have to be mentioned. Just as trees were created with rings (showing an "age"), the stars were created already visible from Earth, dead trees were created to allow mushrooms to grow, etc. Thus, fossils would logically be created as part of the Earth. The sixth day just says that Hashem created all the land animals as they were found when Adam was introduced to the world.
