Why do we take steps before the Shemona Esrei?
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You step forward to meet with the King of Kings.
You first step backwards in case where you are, you can't just step forwards.
If you watch the movie "The Queen" with Helen Mirren, there is a scene that is awesome and quite relevant. The Tony Blair character is about to meet the Queen after becoming Prime Minister, and the page about to let him into the chamber to meet her, explains to him that you do this three step thing before approaching the Queen.
That really caught my eye! I know why! (Also I love about 5 minutes later, trying to break the ice, she informs Blair that her first Prime Minister that she did this meet and greet with was Winston Churchill).
So as Avi notes, this is what we do for a mortal ruler, Kaviyachol, even more so for the King of Kings.
Mechilta, Yisro: The three steps correspond to the three layers of darkness (Choshech, anan, and arafel) that Moshe went through in speaking to Hashem on Har Sinai.