High ISO performance
ISO is the sensitivity to light of your digital camera. The higher the capability, and the better performance of that capability, the better you can shoot in low light situations. If you always shoot outdoors on nice sunny days, or indoors with flash, this may not be a specification that you need to worry about.
But if you want to shoot action, sports, with existing light indoors, weddings where no flash is allowed, or night street scenes, high ISO performance will be very important to you.
Most basic DSLRs have ISO capabilities of 100 to 1600, with 100 being for plenty of light and 1600 being for low light. As you move up in each manufacturer's product line you will see increases in the top ISO available; 3200, 6400 and even an incredible 12,800 in a consumer DSLR! Now just because a camera has that capability does not mean that it has the performance at that ISO.
Most cameras are only capable of producing an image with acceptable noise at a mark below the maximum number. Most that are capable of ISO 1600 really can only go to ISO 400 without getting excessive noise (the bad side effect of high ISO) and even the ones that top out at 12,800 may actually only be usable to 3200. This is still a great feat. If this is a specification that is important to you, you may want to check out some of the camera review sites to see which cameras do better in this regard.
Large and High-Resolution LCD
A 3" or larger LCD on the back of your camera is a welcome addition. For reviewing your shots or zooming in to check focus, the larger and higher resolution will make it easier for you with less squinting. It will also help for the display of all the camera's menus in larger fonts making it easier to read and adjust settings. They also help if your camera has a "Live View" feature which I will discuss next.