I don't see why である is being distinguished from だ even though ではない is included on the page for だ. Furthermore, several forms have been missed, such as でない (traditional negative form of である) as well as であろう (traditional negative form of darou).
Usually used in written, formal works.
One way in which である (dearu) can be used where だ (da) cannot is to modify nouns. e.g. 医者である田中さん (senshu de aru tanakasan) The Tanakasan who is a doctor.
roma-ji is wrong for e.g. in user comments. 医者である田中さん(isha de aru tanaka-san)
I agree with Eeker. It would be better remove English meaning of (formal equivalent of だ [da]).
I think de aru is found in formal written texts. Thesis, abstracts, conference text, just to name a few examples.