How can masculine singular mean theirs?

Steph, 

The use of 'theirs' for 'le/la leur' and 'les leurs' in the lesson, is a feature of English language usage - more completely, it would be their car, their sunglasses. 

There is a significant difference between English and French in describing possession. 

This lesson and example highlights one of the ways in French to describe "possession".

The "basic' possessive pronoun form is determined by the "possessors" - leur indicating 3rd person plural possessors - " they " are the owners. 

However, in French it is the number of possessions that determines whether the possessive pronoun is in plural or singular - hence "leur" indicates one possession, "leurs" indicates multiple possessions - in either case in English, it is ' ... their (something/s). ' or ' ... theirs. '. 

In French, the grammatical gender and the number of the possession/s also determine the final form. of the 'article' - le/la/les - to be used as part of the compound possessive pronoun structure.

(It is slightly more complicated again with the singular possessive pronouns, as they also have different masculine and feminine forms of the pronoun itself - this is covered in the relevant linked lesson)

Worth looking at all the other lessons covering possessive pronouns and adjectives on this site (a few linked below),

 Le mien/le tien/le sien/etc = Mine/yours/his/hers/its (French Possessive Pronouns) 

Le mien/le tien/le sien/etc = Mine/yours/his/hers/its (French Possessive Pronouns) 

Mon, ma, mes; ton, ta, tes; son, sa, ses = my; your; his / her in French (French possessive adjectives)

and if you want, the attached link will connect you to some of the other nuances and intricacies that can arise.  

https://www.lawlessfrench.com/grammar/possession/ 

(As has happened before some of the links are showing the same name when I post, but are from different sites. If they are not working just search in the site for "possessive(s)".

Just to add to Maarten's post:

leur -- many owners, one possession: leur voiture -- their car
leurs -- many owners, many possessions: leurs voitures -- their cars

Note that in English, the possessive pronoun is always "their", regardless of the number of possessions. In French, this changes from leur to leurs.

Here is the second form usage of leur and leurs:

The car, it is theirs. -- La voiture, c'est la leur.
The cars, they are theirs. -- Les voitures, ce sont les leurs.

Again, in English you have "theirs" in both cases, regardless of the number of cars. In French, you distinguish by using either leur or leurs (and the article that precedes it, of course).