«La niña se come la manzana» is not impersonal (there's a personal subject, la niña, doing the action). Se is being used to mark a finished or complete action (the New Grammar of the Spanish Language refers to it as se aspectual or se intensivo), or to emphasize the effort done to complete it, or even to suggest excess. [Source: NGLE, 23.4o;q, 35.7v-y]
This usage is common with "consumption" verbs: those that refer to eating or drinking, mainly (comer, beber, tomar), and also fumar ("to smoke"). An English equivalent would be phrasal verbs with up.
- Los niños se comieron el pastel. = "The kids ate up [all] the cake."
- Me bebí tres latas de cerveza. = "I drank three cans of beer."
- ¿Te vas a tomar ese trago? = "Are you going to have [all of] that drink?"
- Ella se fuma un cigarrillo. = "She smokes a cigarette."
When used this way the "consumption" verbs are often accompanied by words that emphasize the completeness of the action, such as todo, completo, totalmente, completamente, entero, etc.
These same verbs can appear without the pronoun (se, me, te), but the meaning is not always exactly the same, and sometimes the bare verb sounds unnatural. This is what I "hear":
La niña come una manzana.
That means the girl is eating from an apple; she is taking bites out of an apple, not necessarily eating it all up. Also, the sentence simply describes the situation (girl with apple in hand, presumably).
La niña se come una manzana.
That means the girl is eating an apple, from beginning to end; she is consuming it with the intent of finishing it. She's also personally involved with this eating (maybe enjoying it).
There are some other verbs that can take se to show full consumption and/or involvement, for example leer "to read" and ver "to watch":
Me leí todo el libro de un tirón.
"I read the whole book in one go."
Nos vimos una película buenísima.
"We watched an awesome movie."
There are some cases where you cannot use se with verbs of consumption. For example, when making general statements like
- Estos niños no comen verduras. = "These kids don't eat vegetables."
- Ella sólo bebe agua. = "She only drinks water."
- Yo fumo en pipa. = "I smoke with a pipe."