What is the meaning of probabilistic polynomial time adversary?
Yes, but note as below, the probability is not biased.
From the Lindell, Katz book;

An algorithm $A$ is said to run in polynomial time if there exists a polynomial $p(\cdot)$  such that for every input $x \in \{0,1\}^*$, the computation of $A(x)$ terminates within at most $p(|x|)$ steps.
A probabilistic algorithm is one that has the capability of &quot;tossing
coins&quot;, i.e. the algorithm has access to a random source of randomness
that yields unbiased random bits that are independently equal to 1
with $1/2$ probability and to 0 with $1/2$ probability.

Probabilistic Polynomial-time adversary means; An adversary runs in probabilistic polynomial time algorithm.

Different formulation (due to a comment of SEJPM):

A probabilistic polynomial-time algorithm is a probabilistic algorithm that may only perform a polynomial amount of operations including at most a polynomial number of coin-flips.
A probabilistic polynomial-time adversary is then any probabilistic polynomial-time algorithm.