The word “restartable” for C stdlib string functions means the function can return an intermediate answer or error in mid-string, and you can then continue processing the rest of the string. For example, returning a byte count or pointer to where it left off, which you can pass back in. In this case I think the mbstate_t handles that.
It might also refer to the fact that it's not an error if you're lead with a leading byte at the end of the current buffer if you're planning to stream more still.