Eye relief as a specification published by manufacturers is the distance that your eye has to be from the rear of the scope to attain a sight picture. When a range is stated, for example 4-5", it is usually because the eye relief changes as the magnification changes. Leupolds and Trijicons are notorious for this. I don't build scopes, I only use them so I don't know why this is and it is the reason that I prefer Nikon and Sightron over Leupold and Trijicon.
What eye relief is was already mentioned, but that is only really half the story. You've already read about scope shadow as it relates to eye relief. If you have your head too far back, you won't be able to see through it and if you have your eye too far off center from the scope, you won't be able to see through it.
When considering a scope, I also like to consider how forgiving it is, in terms of how far back I can have my head from the optimal eye relief distance AND how far off of center I can have my head and still see through the scope. The forgiveness that a scope will offer varies directly with the size of the exit pupil. The bigger the exit pupil, the more forgiving a scope will be. The exit pupil can be calculated by dividing the size of the objective lens by the level of magnification. I think that a Trijicon 20X with a 50mm objective was mentioned above, so I'll use that as an example. When set to 20X magnification the exit pupil will be 2.5mm, which is small. Really small. At this magnification, it's going to be really finicky about cheek weld and distance of your eye from the bell. At 10X, the exit pupil will be 5mm and that's a pretty good exit pupil. You will get a good level of light at dusk and dawn and it will be more forgiving with regard to cheek weld.
If you think of the exit pupil as a beam of light that is shining through a hole it is easier to understand the effect that it has on what your eye sees. If you poke a hole in a piece of paper with a toothpick (exit pupil), you'll be able to see through it, but only if you line up your pupil exactly with the hole. Now if you poke a hole through a piece of paper with a pencil (larger exit pupil), your eye doesn't have to be as exact behind the hole to see through it. It's the same thing with scopes, generally speaking. Of course, at some point, quality of the glass and manufacturing comes into play too.
I don't want to get flamed or anything, because I know that many on a budget like the DMS-1, but I consider it a step above a piece of junk. The glass is mediocre at best, it big for what it is (12 inches) and it's heavy (weighs a pound). For comparison, my Nightforce 2.5-10X is 12 inches long and weighs just over a pound and is a lot more scope. If the tacticool reticle is what you just have to have, then go for it. You aren't going to find a decent scope with a lit reticle at that price point (except for maybe the Konus). If you want good clear glass for about the same price, I'd look at the Leupold Mark AR, Nikon African and Sightron SII Big Sky 1.25-5X20 (really good prices at manventureoutpost.com).
If this is going on an AR, you might want to keep the eye relief in the 3-4" range. The AR doesn't kick much and the shorter eye relief will make it easier to mount. My scopes usually wind up being mounted with the bell just forward of the charging handle using a cantilever mount. If you have much more eye relief, you'll wind up using a scout type mount that will have the scope way forward. I try to avoid this because it throws the balance of the rifle off and it looks funky.
Oh, I don't know what your budget it, but if you are looking for a good scope with a lit reticle, the newer Trijicon Accupoint, the TR24 I believe, with the 30mm tube has a constant eye relief all through the magnification range. If you don't want to spend that much, look at the three that I mentioned. Of the three, I really liked the Sightron. The Leupold had that thing where I had to change my cheek weld when I dialed up the magnification. The Nikon African was really nice, I just preferred the Sightron. It was built really well and the setting were very repeatable.