An advice string is an extra input to a Turing machine which is allowed to depend on the length $$n$$ of the input, but not on input itself. Turing machines can simulate families of Boolean circuits if they take an advice string of proper length.
The complexity class $${\sf C}/f(n)$$ denotes the class of problems decidable by Turing machines in class $$\sf C$$ which take advices of length $$f(n)$$, where $$n$$ is the size of input. Examples include $${\sf P}/poly$$ and $${\sf NP}/poly$$ (incidentally, $${\sf P}/poly$$ denotes the class of languages decidable by polynomial-size circuits). Such classes are also called non-uniform because the advice strings can be supplied separately for each length without specifying how they are computed. If each advice string can itself be generated by supplying $$1^n$$ to an efficient circuit, then the class is called "uniform". So $$\mathsf{P}$$ can be thought of as $$\mathsf{P}\text{poly}$$ with uniform circuits
It is well-known that $${\sf BPP} \subset {\sf P}/poly$$, but the inverse does not hold, since $${\sf P}/poly$$ includes undecidable problems. Interestingly, even $${\sf P}/1$$ (a polynomial-time Turing machine which takes one bit of advice) includes undecidable problems.