The list represents the possible parses and the remaining input for each. In most cases you might prefer an unambiguous grammar, so a successful parse is a singleton list of a pair of the full parsed result with an empty input sequence.

But parser combinators build your final parser out of little bits, and sometimes those little bits might be something potentially ambiguous, like "any number of leading zeros followed by a number" which needs to parse "0" as no leading zeros and the number 0, but "00" as one leading zero and the number 0.

Non-deterministic parsers can easily blow out with backtracking much like careless recursive descent parsers, though.