This is called a 'placket'. It is found when a cuff is put onto a sleeve, sometimes used as a back neck closure, especially in baby dresses/gowns.
A 'gusset' is a small pice of fabric that is inserted into a seam:example-the bust is too tight and the seams are opened from the sleeve opening to below bust so an oval shape of fabric can be sewn into the opened seam. In this case, you also taper to a point at ea end of the insert to make it least noticeable.
You can stitch very tiny stitches in the seam allowance and then clip to the stitches, Sew your bias strip slowly to the clip (staying in the seam line), then work to the end of the slit. This bias strip is always sewn to the wrong side of the garment. Then it is turned over and sewn to the outside (right side) of garment, making the placket You might get a pucker, but it will be hidden in the fold over. Do some small samples to get the hang of it.

sorry about typos!

Thanks dancingirl. I have heard of a placket. I may have at one time tried to do one of these, but I've been sewing for over 45 years and really don't remember.

This little dress that I am making is a size 4, is sleeveless and has a bodice with 3 buttonholes in front for the opening. I'm just wondering if it really needs this placket, which will be directly in the front center of the skirt where the right bodice front overlaps the left bodice front. Seems to me that when the bodice is open (unbuttoned), that little dress would be easy to put on/take off. I think a placket in that location is going to make the dress tacky looking, even if I do get it sewed in correctly. The skirt will be gathered at the top, so it's not like it is going to be a very tight dress. What do you think?

You can see in this picture that I have attached.

I think the continued opening into the skirt is to allow the waist joining to be large enough to slip over the child's shoulders. If you don't think it's necessary, or is unappealing, you can skip that step or put the entire opening in back. But the placket isn't really that difficult, you can master it. It is exactly as at the cuff of a shirt sleeve. Just re-inforce the bottom of the slit, (I sew very small stitches in a "V" at the bottom of the cu)---clip right up to the thread--sew down one side to the bottom of the 'V'---then raise your presser foot with the needle down, turn the fabric and continue down. It may look like it won't work, but you'll be surprised after pressing. Do a sample.