Basically, when you say a sentence, the sentence itself does not have any implication or nuance that you want some agreement or reaction from the person you are talking to. But by using the suffix -네- (-ne-) in the sentence, you can add some nuance to the sentence that you want some sort of reaction (desirably agreement) from the other person.
For example, you can say, 오늘 날씨 좋아요. (oneul nalssi joayo.) to just deliver the fact that the weather is good today. However, if you want to mean “The weather is good today, huh?” or “I think that the weather is good today. What do you think?” or “I think the weather is good, and I wonder whether you agree or not,” you can say, 오늘 날씨 좋네요. (oneul nalssi jotneyo.)
And sometimes, even when there is nobody around to talk to, or when you don't really want anybody to react to what you say, you can use this structure to express surprise about a discovery, like “Oh, it was here.” or “Oh, it's good.”
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