If you think about a rocking-horse that a child rides on, think about what result is accomplished. A rocking horse is only a mimic of the real thing; no real riding is done. No matter how hard you ride on it, it will never get you anywhere; it is just wasted effort, expended on a fruitless endeavor that yields no results. In Paul's case, unfortunately, it yielded negative results--his fixation, his attempts to use the horse to fix his family's life, and gain his mother's affection, killed him.
Think about all of this in comparison to one of the main themes of the story, which is greed's futility. Lawrence uses the rocking horse as a metaphor to point out how striving for material possessions, and being completely fixated on greed, is a fruitless endeavor that only harms those who chase it. Trying to create happiness out of money doesn't work, just like riding a rocking-horse doesn't produce the real experience. It's a harmful waste of time, a delusional undertaking, bound to fail. The rocking-horse is a metaphor for people's assumption that wealth will solve problems and fix lives. It won't, just as riding a rocking horse won't help you go get anywyere--it just gives you the feeling of motion without being real. Attaining wealth might give you the feeling of trying to achieve happiness, but it won't work.
I hope all of that made sense and helped a bit; good luck!