Why is this festival named after the seven weeks that were counted starting from Passover, which culminate on this day? These weeks build up the bond of love between us and God. We renounce all else for the sake of our love for Him.

The counting of these weeks is similar to the counting of the seven days [free of menstrual blood] before a wedding:

The counting of weeks is to teach us that at the giving of the Torah we became joined to God like a bride entering the wedding canopy…. Now she will direct her love to him alone, and therefore she counts seven days especially for this bridegroom…. In the same way, aside from our obligation to observe the mitzvot, we became obligated to direct our love to Him alone.

The seven weeks symbolize the period of preparation and the bestowal of our love upon God. This is why the festival is called Shavuot:

Since it is not an easy matter for a person to direct his love to God like a woman does toward her husband, God commanded us to count seven weeks [shavuot]. This is why the festival is called Shavuot, that is, the Festival of Weeks, and not the Festival of Days [even though the days are also counted during the omer]. It is to enable us to understand that we must direct our love to God and restrain ourselves [ne’etzar] before Him [to disconnect from all mundane matters in order to concentrate on God]. This is why this festival is called Atzeret by the Sages; this is the purpose of Shavuot. (Netziv, Ha’amek Davar, Numbers 28:26)

Further reading: For more on Shavuot, see A Concise Guide to the Torah, pp. 192, 317, 472; A Concise Guide to the Sages, p. 309; A Concise Guide to Halakha, p. 340.