Some display interfaces, like HDMI and DisplayPort, can carry audio along with video. This audio stream might get played back by your monitor's internal speakers or you might send it to a dedicated "audio receiver", that strips off the audio signal, sends it out via e. g. S/PDIF, analog RCA or even digital (AES/EBU) or analog XLR.
In fact, both HDMI and DisplayPort can even carry a lot more than video and audio. HDMI can carry Ethernet at 100 Mbit/sec. DisplayPort has a powerful "auxiliary data channel" that can carry arbitrary binary data at a rate of currently 780 Mbit/sec, but that is certainly gonna increase in further iterations.