If you search 'Biblical Theology' on Wikipedia, the first sentence you will read is, "Because scholars have tended to use the term in different ways, biblical theology has been notoriously difficult to define." Notable biblical theologian D.A. Carson has often said this himself and in fact he is footnoted on Wikipedia after the aforementioned sentence. In his entry within the New Dictionary of Biblical Theology titled, "Systematic Theology and Biblical Theology", he cheekily writes, "Everyone does that which is right in his or her own eyes, and calls it biblical theology".
That quote was read on syllabus day of a course I took at Moody Bible Institute on New Testament Biblical Theology. You would think that after taking that class that I would have a relatively good understanding of what exactly biblical theology was... but I didn't. Looking back on that course, I would argue that it should actually be titled "A Few of the Professor's Favorite Topics in New Testament Biblical Theology". I didn't leave with an operating definition of biblical theology; I didn't leave with the cohesive grand scope that good biblical theology labors to present.
It's at this point that I realize that I still haven't properly defined what biblical theology even is... welcome to the world of biblical theology!
The History and Definition of the Term 'Biblical Theology'
In all seriousness, before a definition of biblical theology is given it is necessary to see the historical setting that birthed the term. It did not originate from Christians but, rather, non-Christian critical scholars of the Bible. People who were doused in enlightenment presuppositions (and ultimately unbelieving presuppositions) that led them to view the Bible as a document to stand over and examine by the power of Almighty Human Reason. These critical theologians viewed systematic theology (or dogmatic theology) is a pitiful approach to understanding the contents of the Bible. Get rid of all these faith-assuming categories of systematic theology, they said. Don't bring categories to it. Understand the Bible on its own terms. Hence, the discipline was thus titled biblical theology. Of course, good systematic theologians will tell you that it is impossible not to bring categories to the Bible. Nevertheless, from the beginning of the term's utterance, biblical theology was set as oppositional to systematic theology.
However, many pious systematic theologians did not see this opposition to be necessary. At this point it is crucial to understand that where the term biblical theology originated in critical-scholar circles, the approach of biblical theology had existed long before. Theologians like Origen, Thomas Aquinas, John Calvin, and Jonathan Edwards, though they never articulated a definition for the approach, displayed in various ways the seeds of what we might call today biblical theology. Though, the practiced was ransacked by critical scholars who pitted it against systematics. It seems that it wasn't until Geerhardus Vos that there existed an articulate explanation of the approach of biblical theology that saw itself as mutually dependent upon systematics.
Geerhardus Vos was a Dutch reformed systematic theologian who, during his professorship at Calvin Theological Seminary, had already written a five-volume systematic theology when he was appointed Professor of Biblical Theology at Princeton Seminary. A systematics guy teaching biblical theology. Though, it is often said that Vos did not like the term biblical theology (he preferred 'history of special revelation'), he clearly ran with it and would go on to release biblical theological classics in The Pauline Eschatology and Biblical Theology: Old and New Testaments. Perhaps no better definition of biblical theology has been given other than Vos' own definition which he gave in his inaugural lecture at Princeton Seminary, "Biblical theology is that branch of exegetical theology which deals with the process of the self-revelation of God deposited in the Bible."
Indeed, this is where we find our definition. Biblical theology is nothing other than the exegetical witnessing of the organically unfolding process of special revelation in its historic unity and multiformity. Perhaps Vos, who had a keen love for Gal 4:4 and Heb 1:1-2, constantly took the cue of Heidelberg Catechism Q19.
Q19: From where do you know [that Jesus is the mediator]?
A19: From the holy gospel, which God Himself first revealed in Paradise. Later, He had it proclaimed by the patriarchs and prophets, and foreshadowed by the sacrifices and other ceremonies of the law. Finally, He had it fulfilled through His only Son.
The Unhelpful Nature of the Term
The term is not the best one. As I mentioned, Vos himself understood that. The term itself assumes the opposition that those critical scholars wanted to establish between it and systematics. In our current day, it just sounds like you're trying to say that your theology is the best theology because its biblical. Who wants oppose it? What are you going to do, engage in unbiblical theology? Of course, that is how the stage is set and seen by so many today just as it was when Vos inherited the term. Though much progress has been seen in the post-Vos era within the discipline itself... the unhelpful term remains the same. If it were up to him, we wouldn't be using this term anymore but rather be using the more accurate (yet less concise and catchy) history of special revelation. But alas, we have what we have.