Points are used for tutoring services, that are only available on the website, like writing correction and live conversation, and to buy premium lessons. You can buy points or they can be earned by tutoring, referring friends, and sharing lessons in the Library.
If you earn points by providing one of the services mentioned above, you can exchange those points for cash.
Note that a 15% commission will be withheld by LingQ for each tutoring lesson. However, there is no commission for points earned from referrals or sharing lessons.
You can find your points balance here or by hovering over your profile picture on the top right corner and selecting Settings -> and then click on the Points tab.