In terms of acid-base balance, aldosterone stimulates a pump in the kidney (technically, on the intercalated cells of the collecting duct) that normally pushes out H+ ions into the urine. In other words, under normal circumstances this pump has the effect of causing H+ loss by the body, making it more alkaline (higher pH).
From this it's easy to work out what happens in aldosterone hyposecretion: the pump is understimulated, resulting in H+ retention and acidosis. (It's usually mild, however.)
Aldosterone also has some interesting effects on other electrolytes - sodium and potassium in particular - but we'll have to cover that on some other occassion.