A version of Loki who was arrested as a child, escaped, and spent her whole life hunting the organisation that took her, which is a very different life from the one the other Loki had.
Sylvie is a Loki who never had Asgard. She was taken by the Time Variance Authority as a child for a reason nobody will tell her, escaped into a succession of apocalypses where nothing she did could be detected, and grew up alone with one goal.
The series is built on the difference between the two of them. One Loki has spent a thousand years being told he was a prince. The other has spent her life being told she should not exist, and it is the second one who ends up making the decision the whole story turns on.