It is standard cryptographic notation, but the origin might not be immediately clear.
In formal cryptographic papers one reasons over Turing machines. For example, probabilistic algorithm $\mathcal{A}$—which can be described by some Turing machine $M$—has not only an input tape, but a random tape as well. One says that this (binary) random tape is generated by flipping (fair) coins. (Sometimes papers actually say something like “the probability is taken over the coins of the encryption algorithm”.) The notation of the dollar sign (\$) is a nod towards these coin flips, indicating (uniform) randomness.
Notation such as $b' \buildrel\$\over\gets \mathcal{A}(1^\lambda)$ is not uncommon, indicating that a probabilistic algorithm $\mathcal{A}$ outputs $b'$ (note that this output is not necessary unique) on input $1^\lambda$ (usually $\lambda$ denotes the security parameter, e.g., the bit length of a key. The key length is written in unary notation here, which is again related to the polynomial running time of the algorithm in terms of the security parameter.)
The step to use the ‘dollar sign notation’ for sets is now easily made.