The following is where in-development documentation will appear for TidalCycles 1.5.0 and later. For older versions, please see Custom OSC - pre 1.5.0.
Open Sound Control (OSC) is a standard network protocol, ostensibly designed for music, but it's really just an easy way to send numbers and other data across a network. A range of live coding and other systems including DAWs (Digital Audio Workstations), visualisers and mixers are compatible with OSC.
Really the one and only job of TidalCycles is to send patterned OSC messages, most often to the SuperDirt audio framework. It's fairly straightforward to configure Tidal to send OSC to another system. It involves specifying and where messages should be sent to (the target) - and the structure of the OSC data that is sent.
One way to debug OSC is to use a packet sniffer like wireshark. You can put "osc" in the filter field (no double quotes) to filter out everything except OSC packets. If you click on an OSC network packet and expand fields you can find a nicely formatted representation of your OSC message.