Puppets are normally either greater or lesser than human bodies in some way. While they may have greater strength and move as would a human, some flaw in their creation will expose them at some point. Their speech, actions, or appearance will seem wrong or unnatural, and their parts are only mechanisms animated by magecraft and not truly living. Exposing something like blood and muscle sinew from the loss of a limb should reveal the truth. This has led to the saying "Magecraft cannot create an automaton that contains the spark of humanity." that has been passed down since the Middle Ages. Once simply common knowledge, it eventually became a rule of sorts for magi.
Within her various experiments, Touko has managed to create a perfect puppet imitation of herself despite that rule. It is no more or less than herself, and despite most magi striving to seek higher plateaus in the field, she feels that is the state of the art of magecraft. It has brought her current existence into a state of being that can be likened to Schrödinger's cat. Upon first witnessing her creation, she thought there may no longer be a need for herself, and that it, even after she is killed, going on to act as she did no longer leaves any hope for puppeteers to achieve ascension in their craft. Even if her body is destroyed and her soul is severed, the next Touko simply awakens without issue.
Due to the exactness of the puppets, the next Touko will awaken after the death of the previous one. It is possible to stall the awakening by keeping her brain active, even if the rest of her body is destroyed. Her soul often remembers everything up until the point of death, even the pain of her head being crushed by Alba. It is possible that her full will and goals will not be inherited to the next puppet depending on how far the original is from the puppet. The closer the proximity, the more likely she will inherit the original's will, and the further away, as they are stored all over the world, the greater a blank in her memory proportional to the distance will be formed. She normally has a rule of "begin activity after constructing a puppet", though her easily roused nature and lack of patience causes her to go after Alba right after waking.
The transition between the original and the puppet is very smooth, likened to napping and acting as if she overslept by a few hours. Everything she knows stays with her, and determinism dictates that she should take the same actions as her predecessor. She only knows that she wakes when the previous is dead, so she can no longer tell which version of her is the real Touko, the time when she became like that, or if it even matters at all. She then may create another puppet for the sole reason of convincing herself that she is the real Touko. The previous version may have been real or it may be dead, but with only one of her, there is no way to distinguish between them, likened to a quantum superposition-like state that makes all any version of her "fake" in her own eyes. Alba finds the explanation mostly inconceivable, from the method to Touko's state of mind, so she simply tells him to think of the previous one as fake.
Touko has created an alternate puppet version of herself to stay in the Moon Cell, and she can apparently "ditch it" whenever she wishes after her business there is finished. Normally a magus is trapped inside SE.RA.PH until they obtain the Holy Grail, and only one can normally survive. She is not a Master, so she is trapped there unless she takes drastic measures. The difference between her and her copies are miniscule, and her body is one that will self-destruct once she is ready to leave. Hakuno notes her resolve is beyond their ability to comprehend.
According to Francesca, if these puppets replicate not only Touko's memory but even her soul perfectly, this would mean that she has attained the Third Magic. This, however, remains unlikely.
Source: Type-Moon Wiki
