There is a dispute in the Gemora Zevachim (116A) whether Yisro came together with Moshe's wife and sons prior to matan Torah, as is written in the Torah, or did he come after matan Torah. (The Ramban if of the opinion that Yisro came, as it is presented in the text, before mattan Torah, while Even Ezra is of the opinion that Yisro came a year later, after the Mishkan was built). One of the main points of dispute in the Gemora is whether B'nai Noach offered the korban shelamim. Since we are taught that B'nai Noach did not offer shelamim, and Yisro offered helamim, as it says in Shemos (18:12), "And Yisro, the father-in-law of Moshe, took and olah and zevachim". The term zevachim following the term olah, explains the Maharsha, means Shelamim. Thus Yisro's offering the korban shelamim demonstrates his joining B'nai Yisroel (who, as taught in Shemos (24:5), offer shelamim at Sinai) after kabalas hatorah.
The notion that a Ben Noach can not bring a shelamim is discused further by the Seforno who cites Naaman, the captain of Aram, who, when cured from his tzoraas by the prophet Elisha, proclaimed his intention for geirus by saying (Kings II 5:17), "For your servant will never again offer a burnt olah offering or any zevach sacrifice to other Gods, but only to Hashem". Here too the "zevach" following the olah refers to shelamim, and the opportunity that he would first now himself thereof.
Why might it be that prior to Sinai, only olos (burnt offerings) were brought, and after Sinai, B'nai Yisroel were given the opportunity to bring shelamim?
Rav Hirsch zt"l in his commentary on the Torah explains that a shelamim, of which the greater part of the animal has first been sacrificed to Hashem, is also enjoyed by the one who brought the Korban himself. This establishes the truism that worthwhile material enjoyment can itself become a divine service. Moreover, the Torah is a Toras Chaim, and as such can be mekadesh (sanctify and elevate) all of life. It is therefore understandable that there is a mitzvah to eat three meals on Shabbos, for the very act of eating is not looked upon as an end in itself, but rather a type of, "M'shulchan gavoa ka-zachu" (one is benefiting from the table of G-d). Those partaking of the meals can experience the presence of Hashem, through b'rachos, divrei Torah, and zemiros.
It is interesting to note that the Gemora in Pesachim (68b) which presents a dispute between R' Eliezer and R' Yehsoshua. R' Eliezer holds that on Yom Tov an individual has a choice of either eating and drinking or studying Torah. R' Yehoshua is of the opinion that the day is to be divided, half of the day should be devoted to eating and drinking, and half of it to Torah study. While they argue regarding Pesach and Sukkos, the Talmud teaches, "both agree that Shavuos (Atzeres) requires the component of food, as it the day that the Torah was given." (Similarly, on Purim one of the reasons for Purim Seuda (festive meal) is that on Purim there was a re-acceptance of Torah on the part of the Jewish Nation.) Torah provides us with the know-how and ability to sanctify the mundane and hence the offerings of shelamim commenced with with matan Torah. The notion of sanctifying the mundane is unique to Am Yisroel, and foreign to the Ben-Noach.
I would like to suggest another reason for Yisro's bringing of shelamim after Sinai. The Meshech Chochma (Shemos 18:12) suggests that the korban shelamim that Yisro brought was that of a korban todah, a thanksgiving offering. This offering was in appreciation for his being accepted as a convert into the Jewish nation. It is for this reason that the Torah identifies the menu, that Aaron and all the elders of Israel came to eat bread with the father-in-law of Moshe before Hashem." The Meshech Chochmah says that the bread represents the 40 loaves (30 matzoh and 10 chametz) that the Torah prescribes (Vayikra 7:12) as an accompaniment to the korban todah. Moreover, perhaps Aaron's presence is noted to teach us that he came in the official capacity of kohain to receive his share of the four loaves that had a status of terumah and were forbidden to the non-kohain.
Regarding the korban todah, the Netziv, in his commentary on Parshas Tzav, suggests an explanation as to why it is that on the one hand this korban is like kodshim kalim (the lesser sanctified offerings) in that it could be eaten throughout Yerushalayim , and yet, like the kodshei kodshim (more sacred offerings) could only be eaten for one day and one night. (Kodshim kalim can be eaten for two days and one night.) He suggests that the Torah realized that an individual offering a thanksgiving offering could not consume it in its entirety in one day. Therefore, by necessity, he would have to invite others to share his offering with him.
Perhaps this is another unique characteristic of shelamim. It is a vehicle through which one may reach out to others to share a religious experience. At Sinai, when the Jewish nation recited "Naaseh" (Shemos 19:8) it was a communal commitment to Torah. The Meshech Chochmah notes that it was impossible for any single individual to observe all 613 commandments. Some apply only to a kohain, king, or the body of Sanhedrin. It is only together that we can keep all of Torah. To the Ben Noach, olos represent mans' absolute devotion to God. This they can understand. However, that idea of a religion incorporating bein adam lechavero, a direct responsibility between fellow men, was something initiated at Sinai.