This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+2705 forms with similar adjacent characters prevents a line break inside it.
The CLDR project calls this character “check mark button” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: ✓, button, check, mark.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: ✅︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
A check or check mark (American English), checkmark (Philippine English), tickmark (Indian English) or tick (Australian, New Zealand and British English) is a mark (✓, ✔, etc.) used, primarily in the English-speaking world, to indicate the concept "yes" (e.g. "yes; this has been verified", "yes; that is the correct answer", "yes; this has been completed", or "yes; this [item or option] applies"). The x mark is also sometimes used for this purpose (most notably on election ballot papers, e.g. in the United Kingdom), but otherwise usually indicates "no", incorrectness, or failure. One of the earliest usages of a check mark as an indication of completion is on ancient Babylonian tablets "where small indentations were sometimes made with a stylus, usually placed at the left of a worker's name, presumably to indicate whether the listed ration has been issued."
As a verb, to check (off) means to add such a mark. Printed forms, printed documents, and computer software (see checkbox) commonly include squares in which to place check marks.