"home" is just what we're calling the "neutral" position - where the needle goes when 0 width is selected on a zig-zag machine.
most machines provide a choice - you can select left, center or right - so there is no "home" selection. With some, when you set the machine at 0 width, the needle is as far left as possible. When you set any width, the left side of the zigzag does not change, only the right side.
With a LCR machine, if you set Left, then it does the same as above, if you sent Center, then the zigzag will get wider on both sides of the center line, and if you select right - then the right side will stay and only the left side moves wider.
You can get some different looking stitch patterns depending on what setting you use (LCR) when using cams that produce a pattern by altering the width of the zigzag.
I would imagine the mechanism is much simpler if there is only one option instead of three.