Third Person (Omniscient)
Oh boy, is this narrator omniscient. She occasionally pulls back to make some sort of grand philosophical statement, like the almost impenetrable "Minds that have been unhinged from their old faith and love, have perhaps sought this Lethean influence of exile, in which the past becomes dreamy because its symbols have all vanished, and the present too is dreamy because it is linked with no memories" (1.2.1), but more often she's dashing in and out of people's minds, speaking not with her own voice but the with voice of the villagers:
Silas Marner must be a person of the same sort, for how did he know what would bring back Sally Oates's breath, if he didn't know a fine sight more than that? The Wise Woman had words that she muttered to herself, so that you couldn't hear what they were, and if she tied a bit of red thread round the child's toe the while, it would keep off the water in the head. (1.2.5)
This style of writing is called free indirect discourse, and it's a hallmark of a lot of really good psychological writing. As opposed to tagged direct discourse (He said, "I think I'll go out tonight") or tagged indirect discourse (He said that he thought he'd go out that night), free indirect discourse does away with tags like "he said" and goes right for the character's thoughts (He thought he'd go out that night).
With free indirect discourse, you get the illusion of direct access into the character's mind. The narrator almost inhabits the character rather than directly narrating what the character is saying or doing. Free indirect discourse was super popular in the 19th century—Jane Austen is often credited with introducing, or at least perfecting, its use in English. (The French were pretty good at it, too.)
In Silas Marner, the narrator uses so much free indirect discourse that it's surprising when she takes a step back to make her grand philosophical statements. We're left to wonder how close the narrator is to the world that she's describing. Is she one of the villagers, wandering around among them, sympathizing with them, living with them? Or is she standing back at a narrative distance, passing judgment on them?