>>9123070>What are those thigh straps called?Depending which bit you are referring to, either "garter strap" or "garter". The bit that encircles the leg is the garter, whereas the garter strap is what runs up the leg and connects to the bit worn around the waist, known as the "garter belt". They once served a functional purpose for women who wore stockings (especially in an era before pantyhose). They are mostly considered undergarments.
The specific style Botan is wearing is a derivative of a derivative of that original functional version. Anyone wearing her outfit for real would only have these garters and straps for the aesthetic that comes from those old timey undergarments, via a fancier, and still common, presence of garters in various lingerie sets.
>and what is their purposeIn the past, stockings sucked. They were made out of crappier material, weren't as stretchy or grippy, and slid down the leg easily. They still do, but in the past it was worse. To help keep stockings stretched high, you employed one of three strategies:
1. A garter to provide tightness around the leg.
2. A garter belt with straps, clasped directly to the stockings (without a garter encircling the legs).
3. A combination of these: garter belt has garter straps connected to garters around each thigh.
Botan's outfit is the third, but she is (a) wearing it over her clothes, and (b) she appears to wearing hose/tights (connected), rather than stockings (one for each leg), so she has no need for them to hold up anything.