Yup, meristematic cells has the main role here. I'll try to make it simple (I learn it in french, so few terms may be inexact for the purists, so please excuse me). In a plant, there is several type of cells, each types haveing their own role in the plant (photosynthesis, food reserve, water transport, production of toxins, etc). There is a type of cells called meristematic cells, which can be described as 'undecided cells'. These cells aren't anything in particular, they are dormant with no particular task. When growth is needed (leaves expansion/formation, or a plant formation for a cutting), these cells awaken themselves, and 'find a job': some will transform into photosynthesis cells, others in structure holder cells, etc etc. You can compare them pretty much as students which dont know in what domain to study, then when the time comes up (graduation/plant needs) they are oriented to their new job/function.
So, when a cutting is produced, the meristematic cells are transforming (that's why a cutting is always made near a node, this zone have a particulary high ratio of these cells in it) into roots, leaves, etc. In the case of a Nepenthes cutting, most of them will, at the beginning (because these cells are at the base of any plant's growth), form roots, but they can act more widely as in the case of an explant of Saintpaulia, forming whole plants/buds around the leaf part (vegetative piece.
I hope this explication can help, I realize that it is very hard to explain this phenomenon when you are not in your primary language
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