I would say it is a word to add emphasis to the word that follows. Not always negative and not cursing or swearing but often to emphasise when something has annoyed you. It is quite 'old fasioned' in terms of who says it, for example my grandmother is more likely to say something like this than teenagers are.

the word "darn" in the sentence is adverb , meaning : very , extremely,but not very politely way. I get up DARN early in the morning = I get up very early in the morning.

The word "darn" is just softer way of saying "damn". It's similar to saying "kurczę" in Polish, but I'm sure there are differences. It looks like it's used just for emphasis in your example sentence. I don't think it's used in any negative way. You could replace "darn early" with "very early", but it would lose some of its charm. Another example is "darn right!" or "damn right!" in order to express how strongly you feel that something is correct. People sometimes use "darn" instead of "damn" for religious reasons, they simply don't like swearing, or it can even sound folksy or rustic.

kind of a swear word but its not bad like little kids can say it. you can say that darn thing to show you are annoyed but also you can say oh darn it when you forget something

It shows disappointment or dismay similar to damn it.