Quoting the same Wikipedia page (emphasis mine):
If, in every situation, at most one such transition action is possible, then the automaton is called a deterministic pushdown automaton (DPDA). In general, if several actions are possible, then the automaton is called a general, or nondeterministic, PDA. A given input string may drive a nondeterministic pushdown automaton to one of several configuration sequences; if one of them leads to an accepting configuration after reading the complete input string, the latter is said to belong to the language accepted by the automaton.
A concept of determinism is applied to multiple structures in Computer Science, e.g. automata and Turing machines. In general, an automaton is called deterministic when there is exactly one transition from every state. All actions are determined, there is a single computation path, and the automaton either accepts the string or does not.
In contrary, nondeterministic automata may have several distinct transitions from some states. Each transition gives a different computation path, so the path is not determined by the input anymore but there may be multiple paths corresponding to a certain input. There are several ways to define the language with regard to nondeterministic automata, but the most common one is to require having at least one accepting path. (The other way may be to require all paths to lead to accepting state, not a single one, thus replacing $\exists$ with $\forall$; it may be convenient in defining complexity classes like co-NP.)
You may interpret it as guessing: whenever you meet a state with multiple transitions, you make a guess and pick an arbitrary one. The word is accepted if it is possible to make correct guesses and arrive to the accepting state.