Within your pattern you should have a glossary that explains these terms, as they can be different for every pattern. What kind of pattern is it?

Clip back side seam allowance is to make cuts in your seam allowance, perpendicular to your seam, to allow it to spread over curves.

Hard to be able to explain the others without knowing what parts of a garment they pertain to.

Layer seams would usually mean lining up seams when stitching two seamed pieces together so you get a neat sort of seam junction.
Edge finish would probably be a hemmed or overlocked edge? Not sure on that one - what piece is it for?