Na-adjectival form used when something seems likely to exist, happen, or be true. Common in patterns such as ありそうだ and ありそうな話.
That is a plausible story.
There are likely to be problems with this plan.
It seems like there might be some problem.
That sounds like a plausible story.
Formed from ある, written 有る when using kanji, meaning "to exist" or "to occur," plus そう, the suffix expressing appearance or likelihood.