Millard Erickson, in his massive work Christian Theology, gives a simple but rather comprehensive definition:
[Theology is] that discipline which strives to give a coherent statement of the doctrines of the Christian faith, based primarily on the Scriptures, placed in the context of culture in general, worded in a contemporary idiom, and related to issues of life. (23)
What Erickson simply calls “theology” here is more precisely distinguished by others as systematic theology. Wayne Grudem, a theologian who has also written a massive book on the subject (and pretty much a must-have for your library), makes this distinction, and he defines systematic theology as “any study that answers the question, ‘What does the whole Bible teach us today?’ about any given topic” (21).
Though much shorter, Grudem’s definition is, in essence, the same as Erickson’s; they are both good and useful.
Another even more basic way of saying it, with fewer qualifications, would be to say that theology refers to what we think God thinks about something.
Any other definitions for theology that you would suggest? For further reading, you may want to read about theology-ology.