In the time of Kind David 100 people were dying every day due to a terrible plague. The Sages at that time perceived the plague's spiritual essence and instituted 100 blessings a day. The plague stopped.
Even after the plague, the 100 blessing requirement still applies. Many halachic works make an accounting of exactly 100 blessings which are said in the course of every normal weekday.
On Shabbat (and festivals) the accounting is different. This is because the silent amidah prayer on Shabbat has fewer blessings than the weekday amidah prayer. So on Shabbat you need to make up for the 'missing' blessings. You can do so by eating different types of foods, smelling various spices, and saying the appropriate blessing for each one. Or, according to some authorities, you can fill in the missing blessings by listening to the blessings made during the Torah reading and saying 'amen.'
There's a story told about the Brisker Rav, Rabbi Yitzchak Ze'ev Soloveichik, who was once a guest at someone's home in Switzerland. On Shabbat afternoon he asked his host for a banana and an apple, but he didn't eat them. The afternoon prayer, the third meal, and havdalah came and went and still the fruit remained uneaten. After Melava Malka, the mystical meal served at the conclusion of Shabbat, the host could contain himself no longer. Mustering up his courage, he asked his august guest why he hadn't eaten the fruit.
The Brisker Rav answered that at first he had needed the fruit because he was missing two blessings from the required hundred. (An apple requires the blessing for 'fruits of the tree' and a banana requires the blessing for 'fruits of the earth.') However, during the afternoon synagogue service he was called up to the Torah where he recited two blessings: One before the Torah reading and one after.
- Tractate Menachot 43b
- Aruch Hashulchan Orach Chaim 46