About 3,300 years ago, the Israelites left Egypt.

From the day they left Ramses for Succot, until they arrived at Mount Hore

b (Sinai) and stood at the bottom of the mountain to receive the Torah, they counted forty-nine days ('seven complete weeks'). Israel in Egypt was steeped in forty-nine degrees of (spiritual) contamination, and G-d in his kindness removed one degree from them each day until they were completely cleansed at the Giving of the Torah.

An additional significance was attributed to the time of counting the Omer with the death of Rabbi Akiva's twelve thousand pairs of students, over whom we observe certain customs of mourning.

Shavuot

There has never been a great sight to match that one day, which is why we remember it one day every year. (Maimonides, 'Guide for the Perplexed')

The date when the Torah was given is not specified in the Torah.

On the first (rosh hodesh) of Sivan, Israel arrived at Mount Sinai: On the third month of Israel's exodus from Egypt, on that day they arrived at the desert of Sinai. (Exodus 19:1)

There is a dispute in the Talmud between Rabbi Jose, who considered that the Ten Commandments were given on the seventh of Sivan, and the other Rabbis, who said that the Ten Commandments were given to Israel on the sixth of Sivan. All agree that the Torah was given on a Sabbath. However, the Torah fixes the date of the Festival as the fiftieth day of the Counting of the Omer.