A somewhat formal term for a letter or written communication, often used in official or business contexts.
I sent a letter to the customer.
Please contact us by letter.
書状 is an old-fashioned formal word for a written letter or document, while 親書 adds the specific nuance of personal or official authorship by a dignitary.
Compound of 書 (writing) and 状 (document, letter). The exact historical derivation is uncertain, but the kanji combination naturally conveys the meaning of a written document or letter.