Like most scholars' writings, a lot of this stuff isn't originally mine and is borrowed from much smarter folks than myself and I've made attempts to credit them where possible.
There are two dimensions or aspects of theology that you have to acknowledge when attempting to define it, both with their own distinct character—the academic and the spiritual. The academic aspect of theology was defined by 20th century theologian, Aiden Nichols, as being "a disciplined exploration of divine revelation." St. Anselm, an 11th century theologian, defined the spiritual aspect much more simply as "faith seeking understanding." Before we go into what these mean, it’s important not to think of these as two alternatives or options of how to look at the matter, nor even two sides of the same coin. But, rather, they are two poles between which in a tension sits theology proper, which is a balance between faith and reason. If we deny the academic, as is often tempting to do, and rely only on the spiritual, then we deny the necessity of reason, thereby allowing anything prayerful or contemplative to be considered theology. If we rely only on the academic and deny the spiritual aspect, then we eliminate the need for any active faith or belief in what we study, thereby reducing theology to some kind of clinical process or case study.
The academic definition, again lending itself more to a conventional scientific approach, highlights the nature of theology as a science in its usage of terms and bears dissecting: “A disciplined exploration of divine revelation.” By “divine revelation” we mean Sacred Scripture and Sacred Tradition (notice the use of uppercase letters, which indicates the formal scriptures and traditions of the specific religion in question, in this case Christianity)—the Bible and the Church traditions passed down by apostolic succession. “Exploration,” being the bridge and balance between two elements of “divine revelation” (aligned with faith) and “discipline” (aligned with reason), is the elevation of the mind through philosophy to understand divinity, which is the ultimate goal of theology. “Discipline” characterizes the approach to spiritual topics as being well-ordered and coming from man’s natural gift of rationality, namely that it’s philosophical. It then stands to reason that theology is itself a science and that it generally follows (though not in every way) basic scientific guidelines.
Since the Church (as in the whole body of religious believers) accepts the principles of theology by faith, then faith must play a vital role in theological study (again, reason and faith). As other sciences rely on the principles of a higher science, then one has to invest some belief in the higher principles to understand the effects that result from them (e.g., you can’t study biology if you don’t believe the principles of chemistry). Therefore, nothing in theology can be scientific unless we believe the fundamentals to be true—that God (or at least creator) exists, for example. So, the highest fundamental principles come from divinity in the form of revelation in its various forms.
Another theologian from the distant past, Thomas Aquinas, said, “It is necessary for human salvation that certain matters that exceed human reason be known to us by divine revelation.” All he meant is that no matter how advanced we get with conventional sciences and technology, we still can’t know the highest things that are essentially unknowable by humans. However, theology doesn't fill in the gaps of science (lest it create a weak “God of the Gap” scenario), but rather expands that which is beyond knowing through science and what is reasonable through philosophy. Using faith as a starting point, which Aquinas also called “thinking with assent,” is really the only way to actually experience the object of theology (i.e., divinity) and know anything about it. The fundamental articles of faith can’t even be disproved through denial of them. You can really only show the difficulties of their acceptance or denial.
Theology is related to all other sciences in a sort of hierarchy by means of philosophy. The other sciences are necessary as the human spirit is both intuitive and rational, using reason to discover truths by analysis and investigation, thereby organizing those truths in a coherent fashion. So, as each science investigates its respective object and reaches to its higher science, each eventually reaches to the transcendent, which is unknowable through reason alone. Philosophy builds a bridge to the transcendent from the other sciences by mediating their application in a universal way and making them reach to theology. Therefore, there must be a healthy and consistent dialogue between theology and the other sciences, bridged with philosophy, so as to prevent theology from degrading into wild superstition or zealous fanaticism, as well as allowing other sciences to soar to the full heights of what man can know. Philosophy also allows theology to reasonably critique the validity of its assertions, thus validating it as a true science—as Albert Einstein once said, “Science without religion is lame, and religion without science is blind.”