What is the scientific explanation of orange peel or "peau d'orange" texture?

The cancer cells clog the lymphatics that drain the skin, this causes the skin to swell producing skin puckering which is described as "peak d'orange" or skin of an orange.  This term has been borrowed in cosmetic surgery to describe several phenomena, none of which are remotely related to cancer of the breast or any other cancer.  One application is to describe fine dimpling in the chin that is seen is some women.  This has really nothing to do with the lymph system.  It is actually caused by the action of the muscle in the chin on the skin.  Both botox and fillers are helpful for these issues.

Peau d'orange (French for orange peel skin) is caused by cutaneous lymphedema which results in swelling of the skin. The skin is tethered by sweat ducts or connections to muscle that produces dimples in the skin like that of an orange.

Peau de orange skin is usually due to swelling. This can happen with any procedure. Best of luck with your results.