This pattern adds a sense of 'there is something worth noting' or 'I feel that...' about a person, thing, or situation. It's often used when you are struck by a quality or emotion. For example, seeing a beautiful sunset might make you say 'there is something moving about it.' It is not used for simple facts; it carries a subjective, often appreciative or emotional tone.

In terms of grammar, you take a sentence that describes the subject (e.g., '彼の話は人を感動させる') and attach ものがある to the end: 彼の話は人を感動させるものがある. This turns it into 'His story has something that moves people.' The subject is often a topic marked with は, and the clause before ものがある is nominalized conceptually.

This is a written and somewhat formal pattern, but you might hear it in speeches or thoughtful conversation. It is not casual slang. When speaking, you might use it to express a deep impression, but be aware it can sound a bit literary.