During the Amida prayer we stand before God, the King of kings. This is not the case regarding other berakhot and prayers: although all prayers must be recited with solemnity and kavana, they are not on the same level as the Amida, in which we stand before the King. Therefore, the Sages instituted special halakhot that pertain solely to the Amida prayer.
In order to express one’s desire to come closer to God and to stand before Him, we customarily take three steps toward the Amida prayer (Rema 95:1). After finishing these steps, one stands in place and only then recites the verse “Ado-nai sefatai tiftaĥ u-fi yagid tehilatekha” (“My Lord, open my lips and my mouth will speak your praises”; Tehilim 51:7), since that verse is part of the Amida.
One who goes to synagogue or prays in a designated place in her house has already taken more than three steps to get there, and therefore need not take another three steps prior to praying the Amida (Eliya Rabba). Some poskim say that it is proper even for one who already walked to her place of prayer to take another three steps forward, immediately before beginning the Amida, if a significant amount of time has elapsed since she arrived at her place of prayer (Ben Ish Ĥai, Be-shalaĥ 3; Kaf Ha-ĥayim 95:7). However, because it is not appropriate to take three steps back and immediately afterwards three steps forward, one who wishes to be meticulous about this should take three steps back a short time before the Amida, and, after waiting a bit, take three steps forward to begin the Amida (Minhagei Maharil; MB 95:3).