So too do we find, shortly after the account of Maamad Har Sinai and Matan Torah, a second description, which offers us a different perspective on the events as significant to us as is Creation to the world (including us).
There are different suggestions as to why the account of Matan Torah is presented twice. One simple idea is that it becomes clear that all the laws and details of Mishpatim can be seen as part of Revelation at Sinai. This idea is supported by the VAV of V'EILEH HAMISHPATIM, upon which Rashi comments that it comes to state: Just as the mitzvot of the Aseret HaDibrot were given at Sinai, so too were all of the mitzvot of Mishpatim.
Regardless of why, though, let us look at the "what" of this second description of Matan Torah.
First, let's just go back one notch. After the main mitzva-content of Mishpatim, the Torah tells us that we will be escorted into the Land that HaShem has prepared for us - Eretz Yisrael. Two more mitzvot are included for that experience.
Then the Torah takes us back to shortly before Matan Torah. G-d had told Moshe to ascend the mountain... This, says Rashi was on 4 Sivan. On that same day, Moshe told the people of G-d's commands concerning the restrictions during the days before Matan Torah, and reviewed with them the Seven Noahide laws, Shabbat, Honoring Parents, Para Aduma, and other topics that had been presented at Mara (Rashi quoting the Gemara). Moshe then wrote down the part of the Torah from B'reishit until Matan Torah, in addition to the mitzvot from Mara. A Mizbei'ach was built at the foot of Har Sinai. This was on the following morning (5 Sivan). He also erected 12 pillars - one for each Tribe. Firstborns from among the people (they had not yet lost their "kohein-like" status) offered bulls as Olah and Shlamim sacrifices. The blood from the korbanot was sprinkled, half on the Mizbei'ach and half over the people. The Book of the Covenant (as mentioned earlier, containing from B'reishit until Matan Torah and the mitzvot presented at Mara) was read to the people. That was when they (we) responded NAASEH V'MISHMA. Aharon, his sons, and the Elders accompanied Moshe (part way up the mountain?) where they had a holy "pre-Matan Torah" vision.
The Torah then skips to right after Matan Torah, when G-d asks Moshe to ascend the Mountain and remain there to receive the stone Luchot, the Torah, and the Mitzvot that I (G-d) have written to teach the people. When Moshe reached the top of Har Sinai, a cloud enveloped the Mountain. The cloud remained for six days, and on the seventh day G-d called to Moshe. Moshe was to remain there for 40 days and 40 nights.
Among other things, a very significant message from this second account of Matan Torah at the end of Mishpatim is to connect the Aseret HaDibrot with the rest of Torah and Mitzvot, and to connect the experience of Revelation at Sinai with the 40 days/nights that followed. All of Torah is from Sinai.