Why does Edema occur in Kwashiorkor?
Why would decrease in amount of proteins cause Edema? 


Proteins in the blood (esp. albumin, because it's the most abundant one there) cause fluid to come from the interstitial space into the capillary. This phenomenon is called oncotic pressure. On the other side there is hydrostatic pressure on the vessel wall, which causes fluid to exit the capillaries. This hydrostatic pressure gets lower as the blood passes through the capillary, while the oncotic pressure stays the same, because under normal conditions, proteins don't exit the capillary very much compared to their amount in blood.

In the first part (closer to the arteriole), hydrostatic pressure is bigger, so the fluid exits the capillary site, while as you get closer to the venous site, the hydrostatic pressure gets lower than the oncotic pressure and the fluid flow is reversed. (see picture) 

If you lower the amount of proteins in the blood drastically (as in Kwashiorkor) the oncotic pressure is lower and therefore less fluid is reabsorbed from the tissue, which leads to its accumulation there - this results in edema.


  Why doesn't it occur in Marasmus (which is both protein and energy deficiency)?


Sometimes, both features of kwashiorkor and marasmus are present in the patient, which is called marasmic kwashiorkor and the distinction between these two conditions isn't that easy.

However, normally in marasmus, there is also dehydratation present, which balances the effects of decreased oncotic pressure. Cardiac output is usually decreased too, which leads to decrease of hydrostatic pressure, so again, this can counterbalances the decrease of oncotic pressure.