@Rayster
Yeah, you're probably right about that one.
It likely has something to do with identity and the root is the purest form of it. This manga seems to employ the concept of "the power of belief", which is probably somewhat based on Japanese mythology which things can come to existence and/or can become stronger when faith/belief/fear/renown/notoriety increases. However, the root points to the highest form of existence, which is simply existing, and not as a legend, memory, or belief. The MC once asked the girls to believe in him when he was doing that timeline-jumping magic, so it's likely that "the power of belief" is implemented in this story.
MC and his adversary seems to be able to manipulate roots directly. It's basically a reality-bending ability. It doesn't seem like they can create new roots or overwrite anything, but they can merge them or pull them out from a different timeline.