I'm confused as to what you're referring to as 'points'
Microsoft's former eco-system within the 360 used what were called 'Microsoft Points' in order to purchase items on XBOX Live. That has since been retired and replaced by real world currency (no need to make adjustments in your head even though it was pretty simple). The XBOX One doesn't and never has used this system.
If you're referring to gamerpoints which you get for unlocking achievements within games - then no - for the most part they do absolutely nothing except 'look cool' next to your name. It's just a measuring stick to determine how many games you've played and what games you've played. There is a program called XBOX Live rewards (Xbox Live Rewards) that depending on what games you earn achievements in, what games you buy, surveys you take, etc... that can be accumulated for small amounts of credit given back to you.
Otherwise, no - gamerpoints don't allow you to purchase anything.