Time shifting, often 'timeshifting' in MediaPortal jargon, refers to the ability to pause, and shift backwards and forwards while watching Live TV. MediaPortal buffers the TV stream.
When you watch TV, MediaPortal's TV-Server tunes into a channel and starts receiving the TV signal. This signal is then written to a temporary file, called the timeshift buffer (*.ts) by a component called tswriter. The size of the buffer (or number of timeshift files) can be configured and varies between single seat vs. networked systems with one or more clients accessing the server.
For more details on the process, see 'The logic of timeshifting' on the Timeshifting page in TV-Server Configuration.