The doctrine of divine simplicity is a necessary description of God’s infinity. It states that all attributes of the divine nature are coextensive with that nature and indeed, they are the nature. There is nothing between the attributes and the nature. There is nothing that separates them, for that something would need to be other than divine in order to maintain the distinction. Since this is unthinkable- that is, since all the divine attributes are infinite and omni- well, omni-everything- the confession of simplicity is a proper conclusion of the via negativa.
This doctrine is very useful because it helps keep our dogmatic speech orderly and consistent. It forbids any talk of disharmony among the divine attributes, and it forbids giving primacy to any one of the attributes. It should likewise be applied in other loci of systematics to continue to preserve consistency and harmony.
My roommate recently pointed out that divine simplicity is particularly effective as a critique against the position, often espoused by Lutherans, that in the person of Christ there is a communication of attributes. This position argues that the divine gives some of its qualities to the human, and the human gives some of its qualities to the divine. This has long been criticized by Calvinists as a confusion of the natures, even tending towards Eutychianism, and I think the charge basically sticks. To go further, though, divine simplicity forbids the giving of some attributes, but not others because again, all of the attributes are equal with the essence. Therefore, it is simply not possible to affirm the communication of omnipresence, but not the communication of infinity. Ubiquity cannot be communicated without also communicating eternality, and this would be nothing more than to make the created the Creator.
And so we see how Christology affects Theology and how Theology affects Christology.