It means 'lets get a plan started." It might date back to 1930's American Hollywood but am unsure. You would want to say: "lets get this show on the road!" (with the exclamation point). People usually say this when they: (you need all three to say that) 1. Have something planned, 2. When there is enough excitement about starting the plan, 3. Are ready to begin the planed process.

In AmEng, it just means to start doing something. That something could be anything. There does not need to be any excitement about it. For example, two kids sit idly on their beds, their mom pops her head in the doorway and says, “I told you guys to clean up this room an hour ago! Let’s get this show on the road, NOW!” Another version of it is “We need to get this show on the road.”