Since the maximum resolution of a DVD is 480P, they won't show your Animoto videos in their full HD glory of 1080P.
You have a couple of options if you'd like to share your videos in HD.
Copy to a flash drive
The easiest method for sharing an Animoto video in full HD format is to download the MP4 version of your video and then copy it to a flash drive (sometimes referred to as a USB key.)
Most newer LCD TVs and media players have a USB port so you can connect the flash drive and play your video.
Burn to a Blu-Ray disc
A slightly more difficult and less common option is to use third party software to burn a downloaded Animoto video to a Blu-Ray disc. In order to do this, you'll need the burning software, and a Blu-Ray drive capable of writing Blu-Ray discs. You'll also need a blank Blu-Ray disc.
If you're willing to invest a bit of time, here's a tutorial by Dave Doeppel that walks you through authoring a Blu-Ray disc using an Animoto video, and Adobe Encore. http://training.davedoeppel.com/make-a-bluray-or-dvd-from-animoto/