First, let's talk about the Time Traveller as the central narrator – not just because he does most of the narrating, but because it's easier to talk about him. The Time Traveller tells his own story, almost uninterrupted, from Chapter 3 to the sixth paragraph of Chapter 12. It's important to note that he is telling his story after it all happened to him. (Even though, technically, the story is in the future, but don't confuse us.)
The Time Traveller's is the only point of view we have of the future; we never see things through the eyes of the Eloi or the Morlocks. We can imagine that the Morlocks would perceive the Time Traveller as a monster breaking into their underground homes and torturing them with light. After all, they were just minding their own business and trying to eat. So while the Time Traveller thinks the Morlocks are monsters, they might think the same of him. But we'll never know more than the Time Traveller knows, which isn't that much.
Luckily the Time Traveller isn't afraid of looking silly, so he'll often give us his first impressions even when they turn out to be wrong. For example, when he meets the Eloi, he thinks they are childlike (4.2) and that they may be fools (4.5). Only later does he remark on how lazy and dumb they truly are (4.13). He already knows this by the time he's telling the story, but he waits to come right out and say it. In fact, it's only at the end of Chapter 5 that he even gives us the names of the two species (5.40).
For the most part, the Time Traveller only gives us whatever information he had at the time. He often says things like this:
So watching, I began to put my interpretation upon the things I had seen [...]. (Afterwards I found I had got only a half-truth – or only a glimpse of one facet of the truth). (4.23)
While he sometimes hints at more information to come, we tend to be stuck with him and his current state of knowledge. Thanks to his first-person point of view, we are along with him on his journey of discovery.
Now let's talk about the unnamed narrator (whose name may be Hillyer – check out "Characters" for more on that). We've crunched the numbers here at Shmoop, and the Time Traveller clearly dominates as the book's main narrator. In our edition, his narrative takes up 65 out of 84 pages, so he is the narrator for about 77% of the text. So why have someone else narrate the opening and closing sections of the book?
The main effect of the unnamed narrator is to give the reader a point of view outside the Time Traveller's. The unnamed narrator can't tell us what happened in the future, but he can tell us both that the Time Traveller's friends don't really believe his story and that the Time Traveller does look like he's been fighting with underground monsters.
This narrator thus gives us a point of view that we can identify with. He's not a mad genius like the Time Traveller or a jerk like the Editor. He's just an average guy who gives us an average guy's perspective on things. And since the unnamed narrator seems to believe the Time Traveller's story, maybe we should too.