This character is a Math Symbol and is commonly used, that is, in no specific script.
The glyph is a canonical composition of the glyphs There Exists, Combining Long Solidus Overlay. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored. The word that U+2204 forms with similar adjacent characters prevents a line break inside it.
The Wikipedia has the following information about this codepoint:
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.
Quantification in general is covered in the article on quantification (logic). The existential quantifier is encoded as U+2203∃THERE EXISTS in Unicode, and as exists in LaTeX and related formula editors.