This character is a Other Symbol and is commonly used, that is, in no specific script.
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+2733 forms with similar adjacent characters prevents a line break inside it.
The CLDR project calls this character “eight-spoked asterisk” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: *, asterisk, eight-spoked.
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:
The asterisk ( *), from Late Latin asteriscus, from Ancient Greek ἀστερίσκος, asteriskos, "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star.
Computer scientists and mathematicians often vocalize it as star (as, for example, in the A* search algorithm or C*-algebra). An asterisk is usually five- or six-pointed in print and six- or eight-pointed when handwritten, though more complex forms exist. Its most common use is to call out a footnote. It is also often used to censor offensive words.
In computer science, the asterisk is commonly used as a wildcard character, or to denote pointers, repetition, or multiplication.