Asking nicely

-(으)세요 contains 시, a marker of respect for the person doing the action, fused with the -어요 ending. That is why it sounds courteous rather than bossy: you are telling someone what to do while raising them up at the same time. The 으 is a buffer vowel: Korean avoids a consonant at the end of a stem running straight into the ㅅ of 세요, so after 앉 it slips in 으, giving 앉으세요. With a rising voice the same form can also be a respectful question, which day 35 covers properly.

주다 means 'to give', so the pattern is literally 'do it and give it', that is, do it as a favour to me. The first verb takes its -아/어 shape, the same shape that sits inside the -요 form, so if you can say 기다려요 you can say 기다려 주세요. Day 6's 말해 주세요 and day 11's 포장해 주세요 were this pattern with 하다 verbs. The 주세요 of day 11 for 'give me that' and this one are the same verb: one hands over an object, the other hands over an action.

-(으)세요 tells someone to do something for themselves: sit, eat, go well. -아/어 주세요 asks them to do something for you. If you say 사진 찍으세요 to a stranger, you have told them to take a photo, as if they wanted one, so the 주세요 is doing real work. The test is to ask who gains: if it is them, -(으)세요; if it is you, 주세요.