Wait, if you are adding eggs, sugar, and milk with flour and water....are we making a cake?
Well, cakes don't have yeast, but yeah, it would be a very cake-like bread if you put them all in. Maybe oil or butter too. It works kinda like this:
Flour is the base of bread, cakes, and cookies - if you aren't putting in flour it's going to be a custard or souffle instead.
Yeast adds the bubbly airyness to bread
Eggs make it more fluffy without being bubbly/airy, if that makes any sense. Unless you add so many eggs that they overwhelm the four, then it becomes like custard.
Sugar makes it sweet of course, but sugar is also eaten by yeast, so it makes it rise faster.
Oil or butter makes it stay moist after it is done baking. All cakes which have "moist" in the name probably have oil in them. Butter makes a bread denser/heavier without losing its creaminess, while oil produces a more slick and spongy feel. Poundcakes are the heaviest/densest cake and also the cake with the highest percentage of butter.
Milk is basically butter plus water.
Water prevents the bread or cake from burning and enables yeast to metabolize. The general goal of baking is to take the bread or cake out of the oven right when the heat has used up the water, because that's when it's done; if you wait any longer it will start to burn, if you didn't wait long enough it may be gooey in the middle.