>export a video file as avi
What codec are you using inside that AVI wrapper?
Are you using an HD codec when you export, or an SD codec?
Read Bill Hunt on a file type as WRAPPER http://forums.adobe.com/thread/440037
What is a CODEC... a Primer http://forums.adobe.com/thread/546811
What CODEC is INSIDE that file? http://forums.adobe.com/thread/440037
Report back with the codec details of your file, use the programs below... a screen shot works well to SHOW people what you are doing
Welcome to the forum.
Along with the answers to John T's questions, look over this FAQ Entry, as what other information would so very helpful, in helping others help you: http://forums.adobe.com/thread/961741?tstart=0
There are two possibilities. First, you have the incorrect export settings. Second, you haven't told the media player to play the clip full screen.
Both are operator error.
First of all, you probably don't want to export as an AVI. The default for an AVI is probably going to be NTSC DV or PAL DV and the frame sizes are fixed. So you have to change the codec just to change the frame size, and none of the AVI codecs in Premiere Pro CS6 are particularly appropriate for full screen playback. (See John's post above mine.)
You would probably be better off using the H.264 YouTube preset for 1080p. Try that out and come back and let us know how that looks to you. If you really need to increase the default 8Mb/s to something higher, perhaps because you have a lot of action in the video, try 15Mb/s. Just know that the higher the bit rate, the harder for your PC to play it back. You are a video editor, so your PC is more likely to play it back full screen at full speed than any of your customer's computers. If you really, really have to, you can go as high as 25Mb/s. Just be aware that the customer may see it stuttering.