Webster's Dictionary 
(1): ( n.) That department of philosophy which treats of the being, perfections, and government of God, and the immortality of the soul.
(2): ( n.) A vindication of the justice of God in ordaining or permitting natural and moral evil.
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
(vindication of the divine government, from Θεός , God, and Δίκη , justice) . This word dates back, in the sense in which it is now currently employed, no farther than the celebrated essay by Leibnitz, whose first edition appeared at Amsterdam in 1710. It designates the attempt to justify God with reference to the imperfections, the evil, and especially the sin, which exist in the world, or, in other words, any attempt to show that God appears in the creation and government of the world as the highest wisdom and goodness, despite sin, evil, and apparent imperfections.
Leibnitz preceded such evidence with a Discours de la Conformite de la Foi avec la Raison, because a theodicy must evidently proceed on the assumption that reason and revelation do not contradict each other, and that the former has the ability to recognize the facts presented by the latter, whether in nature or in history. As the aim of theodicy is to refute by reason the objections of superficial reasoners against the wisdom and goodness of God, the work necessarily demands agreement between faith and reason. It is consequently the primary object of Leibnitz to show that such agreement exists, or that it must be presumed to exist so soon as a correct view of the idea and nature of reason is entertained. Reason is the "rightful combination" of truths, which we recognize, either directly or by means of revelation and there can be no conflict between it and the truth, which God reveals. There are two classes of truths, and, so to speak, two forms of reason. In a narrow meaning of the word, reason has to do only with such truths as it derives from itself or recognizes without assistance from without; and in this character it contrasts with experience, and also with faith in so far as the latter is based on authority and forms a sort of empirical certainty. Its truths are "eternal and necessary truths," in no wise dependent on sense-perception, and, a priori, such as reason alone can apprehend and formulate, because they are founded on logical, metaphysical, or geometrical necessity. Another class of truths presents to view definite facts, e.g. the laws of nature (verites defait), such as come immediately within the province of experience and faith. This class of truths likewise involves necessity, and is so far set forth within the domain of reason also; but this necessity is physical, instead of logical or metaphysical. The contrary to such truths is not logically impossible and unthinkable, but cannot be because its existence would be an imperfection, a fault. This physical necessity is thus shown to be at the bottom a moral necessity, founded in the attributes of God as the highest wisdom and goodness; and as moral necessity it appertains also to the doctrines of the faith, being ascertainable by reason, and forming ground on which to comprehend and accept such doctrines.
With respect to the creation of the world, Leibnitz teaches that it was the free act of God, performed that he "might most effectually, and in a manner most worthy of his wisdom and goodness, reveal and impart his perfection." He could create only a relative perfection, however; the creation of absolutely perfect beings, i.e. gods, was not possible, and the world and its inhabitants were accordingly created relatively imperfect. This condition of things may be denominated metaphysical evil, whose existence was directly conditioned in the will of God by which was determined the creation of limited and imperfect beings. Physical evil, or suffering, and moral evil, or sin, on the other hand, are not directly willed by God, but only indirectly, as serving to promote the good and secure the attainment of a higher perfection of the "whole," though themselves evil as respects the individual. The ground of metaphysical evil was, therefore, the good which God willed to secure in the creation of limited beings, while that of physical and moral evil is "the better" which could only thus be secured.
To the objection that God might have created a world in which physical and moral should have no place, or that he might have altogether refrained from the work of creating, Leibnitz replies that physical evil may serve to help the world to achieve a higher degree of good; and that moral evil, which is possible because God has endowed man with powers of volition, is likewise so wonderfully controlled as to increase the beauty of his universe as a whole. To the further objection that God thus becomes the author of sin, he replies that sin has no positive cause in so far as it is actualized in consequence of the imperfections of the creature, but only a causa deficiens, which, moreover, does not work sin directly and of its own motion, but only par accident by reason of the existence of a ‘ higher good than sense can recognize or desire. The final objection, that as God foreknew all that is future, and consequently inaugurated a causal connection, which must inevitably lead to whatever may come to pass, including sin; the latter is unavoidable and its punishment unjust, is met by Leibnitz by formulating a distinction between predestination and necessity. No volitional act need be performed by man unless he will. Foreordination is not compulsion; and the intervention of foreordained events serves only to influence the will with motives, and not at all to constrain the will with force.
The review of Leibnitz's work shows that it is far from satisfying the demands of the problem with which it deals. The reason for its failure lies in the philosophical views which that author laid at the basis of his scheme, his ideas of the monads, of God as the primitive monad, of the relations between reason and the will, of freedom and necessity, respecting which see the art. Leibnitz. Nor is this the place to attempt a new and independent solution of the problem of theodicy, which necessarily must involve the development of an entire system of philosophy. Suffice it to say that the general method of Leibnitz must ever be regulative to those inquirers who approach this problem from the standpoint of Christian theism, and that the main attempt must be to separate more clearly between the conceptions of physical and moral evil and connect the former more intimately with morality and the moral consummation of the world-to show more clearly the profound reasons for the necessity by which the possibility of sin is included in the concept of human freedom, and the existence of the latter is involved in the idea of the Food and, finally, to tone down certain theological exaggerations of the power of evil, and present freedom and morality in their gradual development out of the natural life and human naturalness, as well as in decided negative contrast with nature.
Most of the philosophers of more recent times who have treated this subject have approximated more or less closely to Leibnitz, and have endeavored by criticism or modification, either avowedly or silently, to correct the faults of his essay. We can only name a series of the older writers, e.g. Balguy, Divine Benevolence Vindicated (2nd ed. Lond. 1803, 12mo); Werdermann, Versuch zur Theodicae, etc. (Dessau and Leips. 178493); Benedict, Theodicea (Annaburg, 1822); Blasche, Das Basen, etc. (Leips. 1827); Wagner, Theodicea (Bamberg, 1810); Erichson, Verhutn. der Theod. zur spekulitiv. Kosmologie (Greifswald, 1836); Sigwart, Problem des Basen, etc. (T Ü b. 1840); Von Schaden, Theodicea (Carlsruhe, 1842); Maret, Theodicea (Paris, 1857); Young, Evil and God, a Mystery (2nd ed. Lond. 1861). — Herzog, Real-Encyklop. s.v.
The Nuttall Encyclopedia 
Name given to an attempt to vindicate the order of the universe in consistency with the presence of evil, and specially to that of Leibnitz, in which he demonstrates that this is the best of all possible worlds.