What advantages does compression therapy have?

Compression therapy is easy to dismiss as a stocking and a sales pitch. It helps to separate what a published source says it does from what a seller says.

What the source credits it with

my.clevelandclinic.org says: "Compression therapy can improve blood circulation in the legs and reduce pain and swelling."

That is three advantages in one sentence: circulation, pain and swelling. The word "can" marks these as possible, not guaranteed.

Reading further on swelling and veins

Compression is often discussed alongside vein conditions. The Compression Therapy page covers types and benefits. For readers in Mokena or New Lenox with persistent swelling, the guide to chronic venous insufficiency is worth reading alongside it.

The question to ask before you buy or sign

Ask the clinician which of those three advantages they expect for you, and how you would tell it is working. If the answer is vague, ask again before paying for anything.