If you are talking about the eyepiece hood that covers the ocular you view through, a quick answer from my experience is the eyepiece cover thing helps with two things:
1. It helps prevent highlighting the rest of your face when looking through the unit. Not terribly important unless you are hunting smart animals, coyotes especially.
2. Without that cover, I seem to get some "washout" or something that has the ability to make my view less easy to see in both dusk/dawn (low light times) and also during the darkest of the night (no light). With some ambient moon light it doesn't seem to make as big a difference, although it does help tremendously when using it during the daylight hours (don't know anyone who hunts with a thermal during daylight but it is certainly possible).
I am sure more people will chime in with other answers to you, but that's what I have found with thermal devices.