-(으)라고 quotes the instruction or intention behind handing something over, and 주다 is the giving: 찍어 먹으라고 주는 거네, 'they give it to you so you can dip things in it'. Nearly every line here is about food set down for you to use — 이거 잘라서 먹으라고 주셨네, 'they gave us these to cut it up and eat'. It is how you work out what something on the table is for.