This character is a Other Symbol and is commonly used, that is, in no specific script. The character is also known as medical term.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+2695 forms with similar adjacent characters prevents a line break inside it.
The CLDR project calls this character “medical symbol” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: aesculapius, medical, medicine, staff, symbol.
This character is designated as an emoji. It will be rendered as monochrome character on conforming platforms. To enable colorful emoji display, you can combine it with Variation Selector-16: ⚕️ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
In Greek mythology, the Rod of Asclepius (⚕; Ancient Greek: Ῥάβδος τοῦ Ἀσκληπιοῦ, Rhábdos toû Asklēpioû, sometimes also spelled Asklepios), also known as the Staff of Aesculapius and as the asklepian, is a serpent-entwined rod wielded by the Greek god Asclepius, a deity associated with healing and medicine. In modern times, it is the predominant symbol for medicine and health care, although it is sometimes confused with the similar caduceus, which has two snakes and a pair of wings.