I've seen $\mathbb{K}$ in a few places defining affine function without a definition, wondering what it means. For example:
A function $f : \mathbb{K}^m \to \mathbb{K}^n$ is affine if there exists a vector $\vec{b} \in \mathbb{K}^n$ and a matrix $A \in \mathbb{K}^{m\times n}$ such that:
$$\forall\vec{x} \in \mathbb{K}^m, f(\vec{x}) = A\vec{x}+\vec{b}$$
On
It usually stands for field. It comes from German word Körper.
From wikipedia:
In $1871$ Richard Dedekind introduced, for a set of real or complex numbers which is closed under the four arithmetic operations, the German word Körper, which means "body" or "corpus" (to suggest an organically closed entity). The English term "field" was introduced by Moore (1893)
The symbol $\mathbb{K}$ is just a variable, like any other. It does not have any fixed meaning.
However, it is traditional to use the letter $k$ (and variants of it) to denote fields. So, $\mathbb{K}$ would usually denote some particular field which is fixed throughout what you are doing. It's rather lazy to just start using it with such a meaning without including a line like "Let $\mathbb{K}$ be a field", though.