It literally means "the study of being,” but I’m using it in a particular way. When I say something "is" something, and emphasise that by saying that something "is ontologically" something, it means that I am making a fundamental statement about its "nature."
It's a vague concept, I know. I'm not actually interested in proposing a general theory of the nature of reality - I don't think human language and concepts can even do this as we are part of what we're trying to describe and we can't stand outside "it" in order to analyse it. Rather, I'm interested in the question of how we should read the Bible. This entails asking what it "is." The answer to this involves saying things like: it's a composite product of an ancient Israelite culture produced over a long time span.
There is also another element, however, of what the Bible "is," for one finds all over the Bible statements that its purpose - regardless of its human particularity - consists in communicating the will and the identity of God to those who want to know it. It says that this purpose is something that God himself wills, that it is in fact the primary reason for the Bible's existence in the first place, and that God himself makes sure that this purpose is fulfilled within the lives of those who read it. So, if you take this self-depiction seriously, then according to the Bible the answer to the question of what it "is" is that it is a vehicle of divine revelation and salvation. In other words, the Bible sees itself as part of a broader context, a context even broader than the human one, namely the context of a history of salvation in which the eternal God is constantly revealing himself to humanity through this book.
Yet, there is one further step: the Bible also says that what God himself decides to do in our created space and time is ultimately an expression of something that he himself eternally "is." God himself has a "being" but this being is dynamic, not static. The church calls this the "ontological Trinity," because it believes that God "is" an eternally loving relationship of three distinct persons, who we call the Father, the Son, and the Holy Spirit (this, by the way, is what Christians mean when they say God "is" love; this is an ontological statement; God's being "is" the love of the Father and the Son in the Spirit). It therefore follows that the answer to the question of what the Bible "is" is ultimately related to the question of who God "is." Eternally, the Father loves the Son and the Son loves the Father and the bond that unites them is the Spirit. Temporally, i.e. in our created time, this eternal relationship "unfolds" to allow us to participate in the relationship. The Son became flesh and through his work of salvation for mankind by conquering the power of death on the cross he "brings" us into the eternal relationship that exists between him and his father.
This process of "bringing in", however is, from our perspective not yet complete. In other words, those who now in our time put their faith in the Son receive a "foretaste" of a fuller relationship that is to come. This is why Christians are people who are "waiting" for the fulfilment of time, the "kingdom of God" on earth in which humanity can finally enter into the eternal relationship that God is. In the "meantime," that moment between the Son's historical redemption of humankind (around 33 A.D) and his return, humankind itself is to grow in that relationship that has been started but not consummated. And it does this by reading the Bible. The Bible "is" the place where this relationship grows. God already knows us. The Bible "is" the place where he makes himself known to us “in the meantime”, so that we can respond to him in worship and adoration in anticipation of the day when we can finally “come home,” which is into his arms as a son into the arms of his father.
This has consequences for question for how I should read the Bible, which I won’t go into now as I’ve already written a ridiculously long comment! My point is just this: when most people ask themselves what the Bible “is,” and therefor how they should read it, they often just stop at the human bit and so end up reading it partially. Their decision to do this, however, is not only inadequate to the nature of the Bible, it is based on a prior assumption about what “ultimate reality” really is. Whatever that reality is, it doesn’t look like the one I just described above. They are commited to a different "ontology" than the one the Bible witnesses to. This is why the category of “ontology” is so important for reading the Bible. It helps us think about what the Bible “is” in a way that does justice to what it claims for itself.