When I first read this I had no idea of the polemical context into which Warfield wrote, nor of the general state of liberal scholarship which Warfield deals with. At that level I read him very simply - and he still rewards reading in such a way. His concern is to show the nature of the Scriptures as breathed out by God, and does this first of all by the careful exegesis of 2 Timothy 3:16, 2 Peter 1:19-21 and John 10:34f, and concludes with the authoritative nature of Scripture, because of the nature of its author - 'What Scripture says, God says...'.
He goes on to posit an incredibly close relationship between God and Scripture, grounding it upon the fact that the NT is happy to assign to 'Scripture' what was actually said by God (e.g., Rom 9:17), and therefore to argue that what Scriptures says is what God says (not said).
However, Warfield then goes on to address the human nature of Scripture, and the reality of human authorship, all the while wanting to grasp a more organic, more intimate event than what is conveyed by the term 'dictation'. Here we return to the concept of the spiration of Scripture - the divine breathing out, through the totality of human agency, the very words of God.
Warfield spends some pages stressing God's total control in providence over the entirety of a person's life, so that what they (for example, Paul) write is exactly what God intends for them to write. Given this, Warfield goes one step further, grounding inspiration as a mode of revelation. Not just a record of revelatory acts, but as an act of redemptive revelation in and of itself.
As I noted earlier, I didn't understand all this when I first read it. And, to be fair, having skimmed the article to write this, I think there's a fair bit in there that I would want to spend some more time thinking about. But what did influence me particularly was the way in which I came away from reading the article realising that I could have confidence in the Bible, because to do so was really to have confidence in God. Not in the sense that I ascribed divine personality to the Scriptures themselves, but because through them I hear the voice of a loving and speaking and acting God. I could take confidence in what I read.
This was vitally important to me because when I first read this I had not long left a church which had implicitly (and at times explicitly) told me that I couldn't have confidence in the Bible. That it wasn't 'real' in the sense that it didn't all happen like it was written. And even I could see that if that was the case with certain miracles (which was the presenting issue), where did you stop? The virgin birth? The resurrection? My sinfulness? The cross? The reality of Jesus? My eternal salvation?
Warfield showed me that God told me I could trust the Bible. I could trust it because it was his word, and because it was his word, not only could I trust it, I must.