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Toughness is an approximate characteristic, as not all defensive properties are taken into account. A character's maximum Life, Armor, all resistances (though this uses the average of all resistances, so Toughness for endgame may prove to be different for each resistance), passive skills that reduce all damage taken (such as Blur), and some other modifiers, are what formulate his/her sheet Toughness. However, this does not show all modifiers, such as reduced damage from elites, or the guaranteed 30% damage reduction that the Barbarian, Monk, and Crusader classes possess. A player's Dodging chance, while shown as affecting ingame Toughness, shouldn't be taken for granted, as this defense only works for certain attacks.
Overall, this statistic is designed to give players something to orient at when they change items and skills. A higher degree of Toughness makes a character more durable, but without sufficient healing, it can prove harmful to the Nephalem's success. There is no such thing as 'required toughness', as it entirely depends on the player's game style and personal preferences.