You need a referral letter from a doctor to make an appointment at this hospital.
Remember how a 年賀状 is a new year's card? This is another kind of card/letter, but this time it's for an introduction (紹介), making it a letter of introduction.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own. Will help to know 紹介 as well.