The captcha is used to make sure the user is human.
And the email confirmation is used to ensure they own the email address.
You don't necessarily need both of these steps. They're seen most on sites that get a lot of traffic, and potentially a lot of spam. So the decision should be made based on the nature of your site.
For example, it's common to see public online forums require both of these because there's incentive for rogue advertisers to spam your site by posting automated comments. And these two mechanisms are somewhat substantial roadblocks to prevent that. By contrast, there's really no incentive for similar organizations to spam a site that is private in nature.