-거든요 is one of the ways (데요지요, 잖아요) to express speakers feeling and it is used as a sentence endings in Korean.
-거든요 is used when you want to provide background information on your action. This means you use it when you want to tell why you did something or why you didn’t do something.

The English translation of -거든요 is as you see, (because). 거든(요) is attached after a verb or adjective stem Let’s elaborate this from examples.

Someone asks you a question 왜 한국어를 배워요? Why are you learning Korean?
Your reply: 제가 한국사람이거든요. You are providing a very reasonable answer (appropriate reason). – (Because I’m a Korean person.)

Someone tells you: let’s go for shopping/ 쇼핑 하러 갑시다.
Your reply: 돈이 없거든요. I don’t have money. Though its translation is I don’t have money its actual meaning is I can’t go shopping because I don’t have money.

Someone asks you: 왜 기분이 나빠요? Why your mood is not good?
Your reply: 시험을 못 봤거든요. I didn’t do well in the exam ( That’s the reason I’m not happy)

-거든(요) is somehow similar to 데요 because 데요 also provide background information. For example –
If someone says let’s go to watch a movie and you say 저는 바쁜데요. This means you are providing background information (you are busy) and your intention is not to go for a movie.

-거든(요) is also used to say when you want to say let me tell you.

Person A: 너무 피곤해 보여요. 왜 이렇게 피곤해 보여요? You look so tired. Why do you look so tired?
Person B: 어제 잠을 못 잤거든요. Because I didn’t sleep well yesterday./ I couldn’t sleep last night.

Person A: 왜 우산의 가지고 왔어요? Why did you bring an umbrella?
Person B: 오늘 일기예보에서 비가 온다고 했거든요. Because the weather forecast said it was going to rain today.

Person A: 왜 남자친구랑 헤어졌어요? Why did you break up with your boyfriend?
Person B: 성격이 안 맞았거든요. Our personalities didn’t match.

-거든요 vs -잖아요

-거든요 and -잖아요 both are sentence endings.
-거든(요) can be used used to say a reason or background information for something.
저 방금 왔거든요 means I just arrived here (I don’t know what just happened here because I just got here.)

-잖아요 is translated as you know in English. -잖아요 is derived from (shortened form of) 지 않아요.
잖아요 is used to say you know the reason/ you know the situation. (reminding the reason.)
저 방금 왔잖아요. means you know I just got here, too. (The speaker is supposed to know.)

Winter is very cold in Korea. So one person says 오늘 너무 추워요.
Another person says 겨울 이잖아요. Its winter. (You know its a winter season)

But -잖아요 and 지 않아요 have a different meaning. 지 않아요 is an expression used to deny the act or state indicated in the preceding statement.

보통 다 먹지 않아요? means Don’t we usually eat it all?

거든요 conjugation

In present tense: [adjective / verb stem] + 거든(요)
없다 – 없거든요
가다 – 가거든요
먹다 – 먹거든요

In past tense: [adjective / verb stem] + 았/었거든(요)
보다 – 봤거든요
오다 – 왔거든요
가다 – 갔거든요

In future tense: [adjective / verb stem] + ㄹ/을 거거든(요)
가다 – 갈것이거든요

끝나다 – 끝냈거든요.
비싸다 – 비싸거든요.
싶다 – 싶거든
싸우다 – 싸웠거든
떨어지다 – 떨어졌거든
가다 – 가거든요
아프다 – 아프거든요

거든요 is mostly used in the present tense.