The World Wide Web is full of web pages, most of which are unique, and cover different topics than others. Every site has what's called a domain name, or the address that informs your computer of where to route its bandwidth.
Further, each domain name consists of a top level domain - .com, .org, or dot-whatever your site ends with. A site named thissite.com could change its top level domain to .org, .in, or another top level domain, if the site is available, although such a change is technically considered an entirely new website. Webmasters will often run into difficulty in attempting to maintain similar search results when compared to their current site's performance.
One such difficulty incurred is related to backlinks, or hyperlinks found on external, unrelated sites that link to any of the many pages under your current web page's domain. Backlinks are, by far, one of the most important factors that Google and other Internet search engines use in determining which web pages reach the top of their results, regardless of what type of media is searched for - videos, articles, or graphics interchange formats - what nation one's request is coming from, or any other meaningful variable.
Given you're reading this blog post, you've likely already purchased a new domain name - good job!
If you have yet to switch to the new page you're considering, make sure you maintain a holding page, or a site that will gain search results prior to the swap. It's possible to start gaining traffic to the site, even if nothing of value is located on the site you're switching to.
The best way of transferring traffic and ultimately switch sites your business is actively using is to use what's known in the digital world as a 301 redirect, effectively routing all search engine results from your business' currently-used pages. Making sure you transfer over all existing web pages that fall under your domain is possible with the help of tools available on the Internet. If you rely on such programs, make sure they are reputable first.