Quindar tones are an artifact of early NASA communications. NASA used dedicated telephone lines to link Mission Control (in Houston) to transmitters in radio uplink stations around the world, and during Mercury these analog telephone lines occasionally produced enough noise (static, crosstalk, etc.) during 'dead time' to be audible and annoying to the astronauts.
Prior to Gemini, NASA installed remote-controlled 'keying' systems at each uplink station and modified the systems in Houston so that whenever CAPCOM pressed the Push-to-talk switch on their microphone an "intro tone" was generated. The system at the uplink would detect this tone and 'key' the uplink transmitter. When CAPCOM released the PTT switch, an "outro tone" would be generated which would 'unkey' the transmitter. Because the telephone lines would only pass sounds audible to humans, the signaling tone had to be within the human audible range. A notch filter wide enough to catch both start and stop tone frequencies was put on the transmitters, so the astronauts generally wouldn't hear the tones unless the telephone signal was distorted enough to move the tones outside the filter's range. The tone generator and detectors were manufactured by a company named Quindar Electronics - and the sounds, made famous as 'the beep' in NASA audio broadcasts, became known as Quindar tones.
NASA's Mission Transcript Collection notes that in 1998 a new system was installed which, since NASA had moved to digital signalling, used tones which were inaudible to humans to control the transmitters. However, the Astronaut Office complained that Houston staff had become accustomed to the Quindar tones indicating that a transmission was beginning, so the Quindar tone generator (which was still there) was re-enabled.