Hybrid recording is a feature that basically says that the recorder is capable of recording audio from disparate sources concurrently (at the same time).
For example, if a recorder is capable of recording conversations from telephones, 2-way radios and intercoms at the same time, then it is capable of hybrid recording.
To a lesser extent, the same applies if the recorder is capable of recording different types of the same source concurrently. For example, if a recorder is capable of recording conversations on analogue, ISDN and VoIP telephones, then it capable of hybrid recording.
The advantage of hybrid recording is obvious. You only need one recorder to capture conversations from different types of sources, instead of multiple recorders, one for each type of source.