When you put a foot in the door it can't close all the way. And that's where today's phrase comes from. It's literal in origin and the figuratively. Today there are many ways we use the phrase. We use it to indicate an introduction that is necessary, to start small and lead up to a bigger request, to learn something new that will hopefully lead to even newer opportunities, to keep a conversation going, etc. ( source )

One theory to the phrase is military formation and the precise steps the soldiers are required to take. The steps start with the same foot for everyone, if someone starts off on the wrong foot the formation is tripped up - perhaps literally. The other theory is that if one gets out of bed in the morning with their left foot then they have started off the day on the wrong foot.  The different theories are explained here and here .  These days the phrase means anything that starts off badly - projects, relationships, etc - has gotten off on the wrong foot.