Sewing two-sided pieces or spheres, somewhere there is going to be that section left open for turning right wide out. Closing that section with ladder stitch mimics a nearly invisible seam.
Start by turning the item right side out and as you press the item flat, turn in the seam allowance at the opening and press it flat also to make nice crisp edges to sew together.
Insert the needle from the inside of the fabric along the crisp fold just outside one end of the opening. (In this case the white side.)
Insert the needle directly below where the thread exits the white fabric but in the green fabric, again right on the fold. Take a small stitch there pulling the thread through.
Now go back to the white fabric and right above where the thread leaves the green fabric insert the needle and take a stitch in the white. Pull through.
Continue this process back and forth between each side.
For the sake of seeing what is happening, here are the stitches opened up. This is why it's called ladder stitch. The stitches look like rungs of a ladder.
Now to make a point of how this is different from a hem stitch: An invisible hem stitch is more like this where the needle is inserted along that seam line but comes up through the fold of the opposite fabric. Because the stitching is still right on the edge of that seam, it's still relatively invisible.
And here is the ladder stitch completed, closing the opening I left unsewn in this two-sided project for turning right side out. I actually left two hem stitches in since they couldn't be seen anyway.
And that's how it's done. This makes a lovely flat, invisible closing to seam lines left open for turning or turning and stuffing.
I have used other stitches such as that hem stitch and whip stitch, but I am partial to this one. The only thing I find is that the stitches should be fairly small or the closure has a wiggly look to it. If you get the wigglies because you just can't get the stitches small enough, the solution is to simply reverse direction at the end of the opening, sewing a ladder stitch in the opposite direction and bringing the needle in and out of the fabric between your original stitches. This will flatten everything out again.