Sideloading means installing applications from outside the official Android Market. AT&T blocks this ability to prevent people from installing apps that might do things they don't like. (like tethering)

It's more of a minor annoyance than a complete dealbreaker because anyone that really wants to sideload apps can do so with a little 3rd party help.
Sideload Android apps all you want with the Sideload Wonder Machine | Android Central

If we can gain root access to the device through an exploit then even the sideload wonder machine is not needed. It remains to be seen how hard root will be on these new devices.

 

Couldn't have said it better

 

So, if the Atrix is rooted, then we will be able to install any app we want and no longer be limited to the official Android market that AT&T restricts it to? Is sideloading required to install Swype?

 

Root isn't necessary to install non-market apps, the link I posted above is all that is needed for that. I'm almost certain that the Atrix will have Swype pre-installed, I think I remember seeing it in a video but I can't remember the source.

Root will let the user do whatever they want within the OS, like removing worthless pre-installed crapware.

 

I think it was actually the AT&T hot minute video that showed someone composing an e-mail or text or something using swipe, so I'm going to agree that it's probably already on the phone.