면서 들어오다

come in while doing something

"-(으)면서" means "while, at the same time as", and 들어오다 is "come in". So it says what someone was doing as they walked in: came in very nervous, already talking as he came in, came in dancing, came in saying "give me a cup of tea", came in swinging. It also works for entering a role or a country with something attached — came in calling for stronger public education and social integration.