What 𝒷 means
It is a script-style mathematical variable, not a fixed operator.
An equation or definition supplies its meaning. In mathematical notation, a script b labels a quantity its author defines; a different formula may use 𝒷 differently. Script capitals have established uses for operators, functions, and transforms, but lowercase 𝒷 has no field-wide standard reading.
Why encode a script b separately?
To preserve a mathematical style distinction in plain text.
Mathematical printing already used different letter styles to distinguish symbols. Unicode encoded mathematical alphabets in Unicode 3.1 (2001), so plain-text formulas could preserve that distinction. This recorded a notation style; it did not give lowercase 𝒷 a fixed meaning. Script glyphs vary across math fonts. Using 𝒷 just to style ordinary text can disrupt searching, restyling for accessibility, and other text processing.
Don't confuse it with
1Questions people ask
1Why did 𝒷 turn into plain b?
Compatibility normalization can do that: Unicode's NFKC and NFKD forms map mathematical alphanumeric letters to ordinary Latin letters, so software applying either form removes the script distinction.
How to type 𝒷
𝒷\1D4B7Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.