Both. In indefinite forms, barn is the same in singular and plural (a trait shared with most ett-words). For definite forms however, its barnet (sing.) and barnen (pl.).
In this sentence, you can tell from the possessive ("sitt") that it is singular. Had it been plural, the sentence would've been "hon har sina barn".
A child = ett barn.
The child = barnet.
Children = barn.
The children = barnen.
I believe the sin/sitt/sina possessive pronoun can only refer to the subject of the sentence (which can be any gender/number), and since in this sentence the subject is "Hon" the possessive pronoun would be translated as "her", whereas if the subject were "Han" it would be "his".
This is actually something special about Swedish grammar. Swedish distinguishes between a reflexive and a non-reflexive possessive pronoun. English is ambiguous:
"She reads her book" can mean she is reading her own book, or another female person's book. But Swedish can distinguish between these two meanings:
"Hon läser sin bok" (She reads her [own] book)
"Hon läser hennes bok" (She reads [some other female's] her book)
As you may have noticed, there is a pattern to the gender (1st and 2nd person).
eTT hus, miTT, diTT, vårT, erT, siTT hus. eN bil, miN, diN, (er, vår), siN bil. flerA skor, minA, dinA, erA, vårA, sinA skor.
For the main person part, I don't know a good reminder unfortunately.
As I understand it: In the Swedish language, to use a meaning similar to the English 'a/an', (example: 'a' cup or 'an' apple), "en" or "ett" is used before the noun, (example: en cup = a cup or ett glas = a glass). I have been told there is no reason why some words are 'en' and some are 'ett', you just have to learn which is which. It is this part of the word structure (not the end of the word) that indicates ett = sitt or en = sin.
But this is only how I understand it and I could be very wrong.
So just to check I understand correctly...
Min - My (En) Mitt - (Ett) Mina - (Plural)
Din - You Singular (En) Ditt - (Ett) Dina - (Plural)
Vår - Our (En) Vårt - Our (Ett) Våras - Our (Plural)
Er - Your Plural (En) Ert - Your (Ett) Eras - Your (Plural)
Sin - Their own (En) 'Louise eats her own sandwiches' Sitt - Their own (Ett) Sinna - Their own (Plural)
Hans - His (Someone else) 'Leo eats Joe's sandwiches' Hennes - Her (Someone else)
Dess - It's
Deras - Their