In depiction of people from history, some trying to show a historical depiction, others being cartoons, hqve this kind of strings of an uknown material.
Examples:
https://commons.m.wikimedia.org/wiki/File:Coat_of_arms_of_Iceland.svg#mw-jump-to-license
https://images.app.goo.gl/iNwfT2CZ2LgT8AJY6
https://images.app.goo.gl/DTjADRFevqMjjvVWA
I've found under me thrawls through the interwebs that they're called "cross garters", but no more information.
what function does this article of clothing have?
To keep your (equivalent of) socks up. Many styles of hose, worn as leg/footwear before before the invention of clingy-grippy elasticated materials (this is very summarised), needed a little help to stay up and were quite literally tied onto the leg, or they would try to slide or roll down, or otherwise generally attempt escape. As seen in your examples, they were often tied above the swell of the calf muscle and below the knee, though there was a lot of practical and stylistic variation between cultures/time periods/gender/social class/other clothing worn etc. etc. The crisscrossing effect up the calf could be aesthetic, or could be in order to bind looser hose more closely to the leg, for comfort, practicality (nobody likes muddy baggy ankles), or to fit more conveniently under boots.