Very cool! Thank you guys for the explanations.

To "walk someone down the middle" in the metaphorical sense...means to explain something clearly to someone or to give a detailed description about something to someone. In the literal sense (which I suppose you already understand) it means exactly what it says, to walk someone down the middle of a place (a field, factory, path, road etc.) So if someone says, "Walk me down the middle." they either want you to walk them through a place, or they want you to explain something in detail so they can understand it. Of course you can do both at once, literally walk someone through a place (like a factory) while explaining it (equipment) in detail... I hope I helped you bye :)

This means "Walk me down that middle of the country fair as if you don't care that your ex-girlfriend or anybody else sees us. Don't walk to the side as if you're afraid of being seen with me.