Other forms: improvingly
Something that's improving is getting better. If you learn that your sick friend is improving, it's good news.
When your financial situation is improving, it means you've got more money in the bank, and if your grandmother's appetite is improving, it's increasing so that she can enjoy the chocolate chip cookies you made for her. The adjective improving comes from the verb improve, "make or become better." The root of both words lies in the Anglo-French word emprower, "to turn to profit," from the Latin prodest, "is of advantage."