expression, godan verb (-su)
mail a letter; send a letter
Common everyday expression for putting a letter in the mail or sending it through the postal system.
昨日、祖母に手紙を出しました。
I mailed a letter to my grandmother yesterday.
忘れずに手紙を出さなくちゃ。
I have to remember to mail the letter.
手紙を送る also means 'to send a letter' but is slightly broader, including sending by means other than postal mail (e.g., by courier or electronically). 手紙を出す specifically implies putting a letter into the postal system.
Compound of 手紙 (letter) + を (object marker) + 出す (to put out, send). The verb 出す here carries the sense of dispatching or sending something out.