noun
letter of recommendation; letter of invitation; reference
A formal letter written to recommend someone for a job, school admission, or similar opportunity. Can also refer to a letter of invitation, though that usage is less common.
大学院に出願するために、教授に推薦状を書いてもらった。
I had my professor write a letter of recommendation for my graduate school application.
推薦状を同封して履歴書を送ってください。
Please send your resume with a letter of recommendation enclosed.
紹介状 is a letter of introduction, often less formal and used to introduce someone to a third party, while 推薦状 specifically endorses the person's qualifications.
Compound of 推薦 (recommendation) + 状 (letter, document).