A Gateway game:
1. Has a simple rules set
2. Is easy to understand
3. Is easy to play
4. Is engaging.
The combination of the first three makes the game accessible, the last makes a person want to play. I'll go through each of these and give examples.
First, a gateway game should have a simple rules set. I could hand a person a thirty page, black and white rulebook complete with charts and graphs. Or I could hand them the four page, full color rulebook (with pictures and examples) for Ticket to Ride. If everyone is new to a game, this means someone has to read the rules; the shorter they are, the clearer they are, the better. Even now, though I've been gaming a long time and may power my way through the black and white rulebook, I'd rather read the second, shorter rulebook.
Second, a gateway game should be easy to understand. Let's look at two pictures, side by side, and you pick the game that looks easier to understand. Imagine I invited you over and sat you down at a table, and you see one of these two scenes before you:
Obviously the game on the left has a lot going on--boards in front of each player, another board in the middle, wooden bits, cardboard chits, little writing everywhere, cardboard cards with wooden bits sitting on them...a bit daunting. The game on the right? A single board, and a rack with six domino-like tiles sitting on it (actually, if you look at the far end of the picture, there is a scoreboard as well). If I sat you in front of the game on the right, Ingenious, you'd probably have figured that it plays similar to Dominoes; if you were sat at the game on the left, Puerto Rico, you'd probably stand right back up. Intiutiveness--being able to glance at the board and understand immediately what is going on--goes a long way with gateway games, as does being able to compare the game to another more commonly known game. Ingenious plays like Dominoes. Ticket to Ride (the example discussing the "simple rules set" element) plays like Rummy.
Third, ease of play. This is a little vague, but let me give an example. Chess, has an easy rules set (6 different pieces, each with different movement), is pretty easy to understand (capture the king), but is complex in play. People play lifetimes and continue learning new strategies, there are whole books on opening moves. Conversely, it's very easy to sit a new player down to a game of Carcassonne, and tell them that on their turn they're going to draw a tile, look at it, and place it on the edge of the board so it matches. Already they are playing; I can add the small amount of complexity there is to Carcassonne as the game continues--I can then explain on each person's turn how playing one's meeples (the little wooden men) on each component of a tile (roads, cities, fields, and cloisters) leads to scoring points, how to manage your fluctuating supply of meeples, how the game ends and endgame scoring.
Fourth, a gateway game should be engaging. This is more subjective, as what is engaging to one person may not be to another. The theme of a game can be a big part of this--many would say Agricola is an excellent game, but if someone new to gaming asks what the game is about, and you respond "farming," you might get punched in the face (What? Some people take their games seriously). I have family members that may be wary about playing a space themed game, but it would be easier to get them into a high fantasy themed game, and they'd jump on a Lord of the Rings themed game. If you're attempting to recruit new players, it behooves you to know or learn a bit about this people and their interests before attempting to introduce a new game.
There are a several other aspects that make a game a good gateway game, and may fall partly in "being engaging." For instance, a visually appealing game is more attractive than a bland appearing game, and thus more engaging. Playtime is also a factor; if you want to introduce a person to a new game, they're more likely to be accepting if the playtime is 10-20 minutes, rather than the 4+ hours that some games take. I find games that come in around an hour or less are ideal to introduce to new players; I'm sure it's no coincidence that the big three gateway games, Carcassonne, Settlers of Catan, and Ticket to Ride, come in right around one hour.