I think it is first necessary to explain that the digital TV concept of 'channels' is not the same as the analogue TV version.
With analogue TV (the old system), every individual channel (BBC1, BBC2, ITV, Channel 4, 5) had to be broadcast on its own frequency, and in radio engineering this is what is called a channel. The TV (just like a radio) has a tuner which can be adjusted to select just one of these frequencies at a time and then present the information that is modulated onto it. In the early days of television this would have been achieved using a manual tuning dial, then there were mechanical buttons to select one of several pre-adjusted tuning knobs, and eventually we ended up with electronic means of tuning so all you had to do was send a command from a remote control handset.
The advance of digital TV is the recognition that it is possible to transmit more than one TV service on any one broadcast frequency if the picture and sound information is first converted to numerical representation and then encoded in such a way that redundant information is removed (things that repeat, and things that the human visual/aural system would not notice). It is possible to squeeze 4 services onto one broadcast frequency in high definition with excellent sound, or about a dozen services at better quality than the old 625-line PAL system (analogue TV), or many sound-only (radio) services.
The consequence is that tuning into one digital TV broadcast channel produces a data stream containing information for a multiplicity of TV/radio/data services, and this is called a multiplex (abbreviated to "mux"). Extracting the information for one of those services is then a case of computer processing.
Thus, the HDR-FOX T2 includes two tuners, able to tune in to two different broadcast channels (multiplexes) simultaneously and provide their data streams to the rest of the system. It is then only the processing power available and the programming of that computing resource that limits what can be done with those data streams. Those limitations in our case are to record two services and view (with timeshift) a third, from the set of services that are available in the two currently tuned channels.
When watching live, press 'OK' and you will see a list of services (only the TV ones if you are watching TV, scroll down if necessary). If one recording is going on, you will still have a full list to select from. If two recordings are going on, some of the list may be greyed out (presuming the recording services are on different channels). If, when a second recording starts, you cannot continue to watch a third service live, a message appears on the screen to confirm you are happy to switch away in order to record the programme.