The Amidah is the central section of the service -- both literally (since it's section 3 of 5) and spiritually. "Amidah" means standing, and we stand for this section of the service because it's so important. The Amidah is also called the Sh'moneh Esrei, "The Eighteen," because it originally consisted of eighteen blessings: three blessings of Praise said aloud (Avot, G'vurot, K'dushah), twelve blessings said silently that made Requests, then three blessings of Thanksgiving said either silently or aloud. Somewhere along the line, a thirteenth blessing was added in the Requests part, but no one knows anymore which of them was added later!