A double bracket delimiter commonly used to denote semantic interpretation or special sets in mathematical logic and category theory.
Examples
Semantic brackets notation in formal semantics
\llbracket \text{cat} \rrbracket = \{x : x \text{ is a cat}\}
Matrix with double brackets notation
A = \llbracket a_{ij} \rrbracket_{n \times n}
Interval notation in some contexts
\llbracket 1,n \rrbracket = \{1,2,\ldots,n\}