A jigsaw, you see, is the same thing as a scroll saw, and the name comes from there.
Literal
Jigsaw [as-for-とは] scroll-saw [gen-の] thing is-[and-で], name [gen-の] origin [topic-は] there [from-から] comes-[from-の].
A definition sentence. とは ('as for') here introduces a definition. ジグソー is the loan 'jigsaw' (a type of saw, not the puzzle). 糸鋸 ('scroll saw') is the native Japanese word. の事 ('the thing of, equivalent to') is a common formula for equating A with B. の at the end is the feminine/soft explanatory ending. ~からきている ('comes from') is a set expression for etymology or origin.