"Cutting" meaning?

Cutting = a piece cut off from a plant that can be used to grow another plant of the same type

Cambridge Dictionary

In this case the cutting is an analogy for the idea of the show. Codron’s interest in the idea helped give life to it. It grew and expanded into the show that it eventually became. Just as a small cutting, if suitably planted, will root and grow into the final specimen plant.

The use of take root rather than took root is an interesting point. The answer may be that during the period that is being recalled (“from that day ...”) the author experienced the taking of root as something happening in the present during that period.