Context is always important. But based on what you posted - the speaker has perhaps been listening to someone explain a situation, some gossip, a rumour etc and believes there is even more to this situation than they have currently heard

Imagine you are at a party. You thought your friend was going to come with his wife but he arrives alone. You know that they have not been getting along well lately. You ask him where his wife is, and he says, she's staying with her mother. You could say 'Sounds like there's a story there,' i.e. he gave you a short answer, but there appears to be more to the situation.

A "story" is an account of events, be they imaginary or real. Those events can be recorded in writing, or merely told through speech. When that happens, you are "telling a story". The meaning of "there's a story there" is that based on whatever it is that "there" represents, one could write, or tell, a story.