I'm not ashamed to admit I only played Nuts & Milk because of the word "nuts" in the title. I'm not even ashamed to admit my initial impulse to use the level editor to draw dirty pictures. I am ashamed to admit that I lack the artistic talent to do it.
Milk's girlfriend is locked in the house at the top of the screen. Milk is the pink blob. The only way to get to her is to collect all the fruit on the screen, but Nuts doesn't want that to happen. Nuts is the blue blob. I don't know why Nuts feels the need to cockblock poor Milk like that. Video games didn't have backstories in 1984. They were pretty much all Girl Needs Help. Hero Help Girl. No Ask Questions.
Really, this is just Lode Runner without the greed and cannibalism. Those have been replaced with implied sex. Once Milk gets to Milkette, the house closes back up and a big heart appears. I shouldn't need to draw a picture for you to figure out what's going on in there.