This character is a Other Punctuation and is commonly used, that is, in no specific script. The character is also known as apostrophe-quote (1.0), single quote and APL quote.
The glyph is not a composition. Its East Asian Width is narrow. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. In Hebrew text this single quote joins with other Hebrew letters to form a word. U+0027 prohibits a line break around it. The glyph can be confused with 77 other glyphs.
The CLDR project calls this character “typewriter apostrophe” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: apostrophe, quote, single quote.
The Wikipedia has the following information about this codepoint:
The apostrophe (' or ’) is a punctuation mark, and sometimes a diacritical mark, in languages that use the Latin alphabet and some other alphabets. In English, the apostrophe is used for three basic purposes:
The marking of the omission of one or more letters, e.g. the contraction of "do not" to "don't"
The marking of possessive case of nouns (as in "the eagle's feathers", "in one month's time", "the twins' coats")
Use as a single quotation mark
It is also used in a few distinctive cases for the marking of plurals, e.g. "p's and q's" or Oakland A's.
It is also used informally to indicate the units of foot, minutes of time, and minutes of arc, although in these uses, the prime symbol is generally preferred.
The word "apostrophe" comes ultimately from Greek ἡ ἀπόστροφος [προσῳδία] (hē apóstrophos [prosōidía], '[the accent of] turning away or elision'), through Latin and French.