The weather stripping is the black rubber pieces in your door, they help fill the gaps in the door and seal it tight so that the elements can't get in. Removing it may cause undesireable results, but there is a TSB because of wind noise problems. Here's the link to that TSB. http://www.hmaservice.com/webtech/iindex.asp?id=394888628#_394888628
I think he may be talking about the weather stripping under the hood. There's two pieces, one at the front, and one at the rear, or cowl-area of the hood. Removing these will promote a cooler engine bay, and as far as I know, the only drawback is that your engine bay will get dirty faster.