Sign language (also referred to as gestural language) was a language where communication occurred through hand movement, instead of sound. As a language, the use of gestures and hand signals pre-dated the spoken word in most cultures, the major exception being the Leyrons of Malkus IX who actually developed a written language first. In some cultures, sign language was accompanied with fingerspelling and speech on lip movement.
Sign language was permitted on Betazed for the joining ceremony. When Victoria Miller and Lwaxana Troi were debating on who should officiate at Wyatt Miller and Deanna Troi's wedding in 2364, Lwaxana proposed that her valet Homn would do the officiating. Steven Miller argued that Homn couldn't speak to which Lwaxana responded, "He is quite adept in the act of sign language." (TNG: "Haven")
While on a mission in the Ramatis system in 2365, Lieutenant Commander Data learned and stored five different forms of sign language in order to communicate with Riva, a deaf mediator from Ramatis III. Lieutenant Worf found the concept of sign language interesting, as its qualities of being both silent and covert could be useful in the field. (TNG: "Loud As A Whisper")