The "become one" is Mu's unique skill "shared senses". It lets Mu form a link between her and someone else, letting her share skills with that partner.
It's pretty damn powerful if you consider that in this world people only get a handful of skills. No game-like cheats of having multiple skill trees allowing someone to become a master thief and an archmage at the same time (*cough*Skyrim*cough*). Mu can share her skills but also receive the skills of other temporarily.
The story appears to be that she suffered from using that ability and was abandoned so can only use this with someone she trusts completely. Touru was the first to gain that level of trust as a father figure for her.