According to Jim Recap: A Vast Difference
After Cheryl and Jim have a pregnancy scare, they decide that there is only one thing to do. Strangely, they have markedly different opinions on what that one thing is. Jim's opinion is that Cheryl should practice birth control, while Cheryl's opinion is that Jim should have a vasectomy - which leads to perhaps the most racy title in the series, a play on vas deferens - the tube that delivers the male seed to the female during reproduction. Naturally, Jim isn't too keen on this idea, but at least initially, he agrees. It doesn't quite go as planned, however.
To begin with, Jim starts fiddling with the equipment on the table when he is in the operating room. He promptly breaks something. But that doesn't have anything to do with it. It's when the doctor comes in carrying a large needle and Jim isn't sure about where it's going to go that he promptly chickens out. When he gets back to the waiting room, Cheryl is so proud of him that he doesn't have the chance to tell her that he didn't do it, and naturally the attention he is getting doesn't make him anxious to tell her that he didn't do it either, so he just goes with it.
As luck would have it, he continues to roll with the scheme for a few days, until he finds out that he has to go back in for a follow-up appointment to make sure that everything did what it was supposed to do, and that's when it all starts to unravel. Not because everything is working, but because everything isn't working. It's like he actually had the operation - but he didn't. And because the technician keeps saying "low sperm count", which just gets Jim mad. So he tells Cheryl.
When they get home, they talk about it, and the real truth comes out - he just wasn't ready (not mentioning the needle or where it was going). Somewhat surprisingly, Cheryl says that it was okay, because she wants another baby, and they decide that they want to try for one. Mostly because Jim says that Cheryl does all the work anyway - he just needs to learn another name. So they decide to try for another baby (in The Clock in Season 4, they decide that they actually don't want another baby).
