Rooting is similar to jailbreaking, but the terms are not to be used interchangeably unless you want to out yourself as being ignorant.
Jailbreaking (most commonly used when talking about iPhones) simply means allowing the user access to applications Apple would let them near.
Rooting (usually in reference to Android phones, because of how their OS works, Linux-based) will allow you to acquire applications that may not be allowed by your service provider (usually via sideloading, which some carriers don’t allow), but rooting is much more than just allowing yourself access to different applications. Rooting is essentially giving the user “super user” access to the phone. With the right set of tools and a rooted phone, you can just about any and everything you could want with the phone.
Here is an article explaining the difference and it’s on a site you should become familiar with if you’re interested in rooting your phone.