Irresistible to first answer the question in the title:
It is used for entering characters that are shaped like this § and ± as defined in unicode
U+00A7 for section-sign and
U+00B1 for plus-minus sign.
Then more seriously:
Keyboard layouts are for a very large part historically grown and evolved.
British needs are a bit different than American needs. Americans most often only need the old Peso symbol $ and while £ is most often needed in insular designs the still close relationship with the continent also requires the €-sign. All those keys have to be placed somewhere and somehow shifted around among a limited number of available keys according to local demand.
That need seems high enough for other layouts to opt for a section sign in said place (Finnish SFS 5966, Hungarian, Dutch and then some.)
The British Standard BS 4822 is old and small and it, as well as the international ISO, only defines non-binding recommendations just like the German DIN 2112 and 2137 (which dropped the requirement for a very special Shift 5 a while ago). Apparently there are at least three keyboard layouts for Macs available for (British) English users, two of them with the marked as unusual § position (UK and US-International) all differing from one another and the PC standard.
Before the world settled mainly on the two blocks for computer input of Wintel vs Apple there were even more keyboard layouts around, often differing in very peculiar ways. Since Apple has a keyboard layout tradition that dates back to before the IBM PC they were on a different path of dependencies. Although Apple's earliest attempts on the European market did not include such a sign.
Depending on intended usage one layout has advantages and disadvantages over the other. English speaking programmers have different needs than French novelists or German lawyers.
Who needs the plus or minus sign?
The plus-minus sign is not that specialised as the OP's question implies:
- In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negation of the other.
- In experimental sciences, the sign commonly indicates the confidence interval or error in a measurement, often the standard deviation or
standard error. The sign may also represent an inclusive range of
values that a reading might have.
- In engineering the sign indicates the tolerance, which is the range of values that are considered to be acceptable, safe, or which comply
with some standard, or with a contract.
- In botany it is used in morphological descriptions to notate "more or less".
- In chemistry the sign is used to indicate a racemic mixture.
- In chess, the sign indicates a clear advantage for the white player; the complementary sign ∓ indicates the same advantage for the black
Especially users in science and engineering seem likely to request a more prominent placement or reachability, whereas statistics also imply government actors with wants that might signify demand for that character. All these simultaneously form an important group with quite a big say on the formulation of said standards or specialty layouts.
Who is in need of a section sign?
The paragraph sign ¶ is indeed very rarely seen if you turn off "show invisibles" in your preferred editor. Confusingly, the German name of § is also "Paragraphenzeichen" as well as paragraph sign in Canon Law.
Usage of especially the section sign is still very common in law and governance (the biggest customers often restricted to using standardised tools) but also writers of novels and quite a bit of non-fiction. Especially theologians still cling to a very unsightly tradition to use it throughout their books (quite recent example).
Since usage of said sign in British publications is indeed quite uncommon there are not much explanations left.
In short: historical path dependencies, local needs at the time of standardisation are the general, main reasons; Apple engineers deciding this might be a good idea the other.