thread needle, sew stitch, string
紉 centers on joining things with thread or cord: threading a needle, sewing stitches, or tying with string.
紉 combines 糸 (thread) with 刃 (blade), likely suggesting the action of threading a needle or cutting thread for sewing. The exact historical development is uncertain.
The left side 糸 is thread, and the right side 刃 is a blade. Imagine using a sharp blade to cut thread and then threading a needle to sew stitches.
For ジン, picture a sewing machine making a sharp 'zzz-ing' sound as it stitches: zzz-ing -> ジン, and the thread runs through the needle.