It's unfortunate that they've developed a scariness feeling associated with them. They can be used in strange ways, but simple uses are quite approachable. One way to think of them is like implementing an object-oriented interface. You know it's an object, but you can't do anything with it except use the methods of the interface.
---
{-# LANGUAGE ExistentialQuantification #-}
data Square = Square ...
data Circle = Circle ...
class Perimeter a where perimeter :: a -> Double
instance Perimeter Square where perimeter (Square ...) = ...
instance Perimeter Circle where perimeter (Circle ...) = ...
-- The 'a' is hidden here. The interface is defined by the class constraint.
data Perimeterizable = forall a . (Perimeter a) => P a
-- This is the accessor method for things Perimeterizable.
getPerimeter (P x) = perimeter x
vals :: [Perimeterizable]
vals = [P Square, P Circle]
perims = map getPerimeter vals
---
Regards,
Sean