If something is plausible, it's reasonable or believable. Things that are plausible could easily happen. A woman becoming President is very plausible. A giraffe becoming President is not.
Plausible things are not far-fetched at all. Things in fantasy stories — such as wizards, dragons, and unicorns — are not plausible. On the other hand, some things in science fiction stories might be plausible: who knows where spaceships will eventually go? If something really seems like it could happen, then it's plausible. One of the many tricky parts of life is figuring out what's plausible and what's not.