They could've just titled this book "Beatrice" considering how tightly the story is told from her perspective. (To be fair, it is titled Divergent and that's almost the same thing as naming the book after Tris.)
But check this out: not only is the story from Tris's perspective, but it's told in the present tense: "I open my eyes and walk to the front of the observation room…" (29.30). That puts us not only in Tris's head, but it puts us in her head at the very moment when she's going through all this crazy stuff. What will happen in the observation room? We don't know because Tris doesn't know yet. Imagine this book being told in the past tense (which is more common for most books); in that case, Tris could tell us (or hint or foreshadow) what will happen in the future since she would have already lived through it.
One benefit of the first person, present tense style is that Tris can tell us in every moment how she's feeling. So we can watch as her feelings change or become clearer. When she's choosing her faction, in one moment, Tris is sure she has to choose Abnegation (5.57) and a few moments later, she chooses Dauntless. If we were watching this from the future or from another point of view, we might not see that struggle.
But there is one downside to the first person perspective, which is that Tris may not always be right about what's going on around her. For example, in chapter 13, Tris protects Al by volunteering to have knives thrown near her and Four keeps "taunting" her (13.67). She thinks he's being a jerk—that's what it looks like from her point of view; but as he tells her later, he was actually trying to support her by reminding her of the generous, good thing she was doing (24.77). There are several moments like that, where Tris either misses or misinterprets what's going on. And since we see everything from her point of view, we have to be able to roll with these changes—just like Tris.
In some cases, we even need to be able to see when Tris isn't being truthful with herself. When Tris goes through Four's fear landscape, for example, she notes that "he slips both arms around my waist. I smile at the wall. I am not enjoying this. I am not, not even a little bit, no" (25.69). Yeah, right, Tris, tell us another one. It's pretty clear to us that she's lying a bit here—not only is she smiling, but she has to repeat the denial several times. It's not hard to read between the lines.
And that's another effect of the first-person point of view: Tris sometimes can't be trusted because she's either wrong or lying to herself, so we have to be alert to these problems in her narration.