Paul is Ma's brother. Since she disappeared, he's married Deana and together they've had a young daughter, Bronwyn. Because Ma remains distant from her family after she gets out of Room, we don't see much interaction between her and her brother, but Paul does take Jack on a very eventful trip to the mall.
That visit is darkly comedic at times, like when Jack inadvertently steals a Dylan the Digger book, and traumatic at others, like when Deana slaps Jack and cuts him for touching Bronwyn's private parts.
The private part incident is especially confusing to Jack because Deana tells Jack "we don't touch each other's private parts, that is not OK" (4.1480)—but then she proceeds to clean Bronwyn's private parts. Jack and his mother still bathe together at this point, so he hasn't developed this concept of "privacy" when it comes to bodies. Paul and Deana also try to enforce gender norms on Jack, like when Paul wants to buy a backpack "that's not pink" (4.1422) for Jack, but it's not the Dora backpack that he really wants. C'mon, Paul. Diego is cool, but Dora is where it's at.
However, Jack learns to be comfortable with Paul and Deana the more he adjusts to society. It's nice that Paul calls Jack "buddy" (4.1382)… at least it is once Jack figures out what it means. As Jack accurately observes, "I think buddy is man talk for sweetie" (4.1382). The last time we see Jack and Paul together in the book, they're playing together with a soccer ball. Jack needs all the support he can get, so we're glad Paul is there to offer it. It'll be a journey for them both.