In general parallel thinking is a further development of the well known lateral thinking processes, focusing even more on explorations — looking for what can be rather than for what is.
In adverserial debate the objective is to prove or disprove statements put forward by the parties (normally two). This is also known as the dialectic approach. Practitioners put forward as many statements as possible in several (preferably more than two) parallel tracks. This leads to exploration of a subject where all participants can contribute, in parallel, with knowledge, facts, feelings etc.
Crucial to the method is that the process is done in a disciplined manner, and that all participants plays along and contributes in parallel. Thus each participant must stick to the specific track.