Besides the nerdy, cheesy aspects of the holiday, it is also the holiday for converts. Quite honestly, I don't understand why Shavuot gets such a short shrift in the Jewish world. It's the day when we became the Jewish people and accepted the Torah. Why do people treat Shavuot like it's just a tag-along to Pesach? I was most impressed to see it described as "the neglected stepchild of chagim."
There are two primary stories about Shavuot that relate to converts. And if you want to, you can think of the acceptance of the Torah at Har Sinai (Mt. Sinai) by the Israelites as the original mass conversion. Before, they were Israelites. After, they were the Jewish People.
The most common story about converts and Har Sinai comes from the Talmud. It relates that the souls of future converts all "stood at" Sinai with the Jewish people. Our souls were present just as much as the bodies of the Israelites who fled Egypt. This idea comes from Devarim (Deuteronomy) 29:13-14:
"Not with you alone do I seal this covenant and this oath, but with whoever is here standing with us today before Hashem our Gd and whoever is not here with us today."
A very traditional view of this story is on the Aish website. For a very different view of this Talmudic explanation, read "Perfection": Human Accomplishment - Not a Jewish Birthright (mid-way down the page). Ohr Somayach describes the "procedures" of conversion as a reenactment of the revelation at Har Sinai.
On the other hand, there is a story that praises converts for seeing the truth of Torah and choosing Judaism without needing the awe and fear that the Israelites experienced at Har Sinai. The Jewish people required lightning, earthquakes, and even the mountain being held over their heads. But converts believe without needing any divine "nudging." Despite my awesome Googling skills, the idea of converts physically standing at Sinai overpowers any other narrative on the internet. I apologize for not giving you sources to read about this story.
Of course, Shavuos is overtly about conversion since we read the Megillah of Ruth. Someone asked me about Ruth on the blog's Facebook group recently. I never thought about it before, but I've never been particularly attached to the story of Ruth. But why? After some thought, I came to a conclusion: "Every convert's story is SO different and intricate, but Ruth's is so short. In a way, the description of Ruth's journey is the kind of description most born-Jews would give describing a conversion. [Because they have not heard her particular history.] Because I've been/am going through it, I know there must be more to the story." But every year, Tikkun Leil Shavuot allows me to hear new ideas and stories to challenge my own preconceptions and grow in my Torah knowledge.
Chag sameach! See you on the flipside!