As I understand this, the "fasting" that is forbidden on Saturdays and Sundays (with the exception of Holy Saturday) is the strict fast of not eating anything until sundown. (This prohibition of fasting on Saturdays except for Holy Saturday explains why Holy Saturday is the only Saturday for which a Vesperal Divine Liturgy is prescribed.) Alluding to greekchristian's response, not eating meat or dairy is more the definition of "abstinence," which is still required of us even during the Saturdays and Sundays of Lent.
Exactly the way Fr. Dad explained it to me awhile ago.