Symbolism, Imagery, Allegory
Apart from hanging out with his coterie of women (including his mother, Mrs. Morel), Paul's biggest amour is painting. And he's not half bad at it either. Every time the book mentions painting, Paul seems to be winning some new prize for it.
His painting is opposed to the commercial world that Paul hopes to avoid. As the narrator reveals to us:
He was quite a clever painter for a boy of his years, and he knew some French and German and mathematics that Mr. Heaton had taught him. But nothing he had was of any commercial value. (5.61)
In this text, painting represents Paul's sensitivity as an artist, and his tendency to look at the world in a more romantic way than "normal" people. Art also represents his ambition to do something with his life that isn't "common," like the menial work he ends up doing at Mr. Jordan's factory.
Paul's painting is also the main focus of his mother's pride in him, since she yearns for Paul to distinguish himself in some way from others. When Paul turns out to be an excellent painter, his mother is over the moon about it. At first, she can't really believe his success:
"Name—Paul Morel—First Prize." It looked so strange, there in public, on the walls of the Castle gallery, where in her lifetime she had seen so many pictures. And she glanced around to see if anyone had noticed her again in front of the same sketch. (8.100-8.101).
But, over time, Mrs. Morel trusts in her son's ability and uses it as a way to feel like she's just as good as any rich woman in her county. So, painting represents a lot of the characters' hopes and dreams in Sons and Lovers. It's their golden ticket out of Normal Town, and into Greatness City.