It really depends on your meaning. Do you mean what makes me like a game, or do you mean what would impress me in a game that I either like or at least like enough to keep playing? Since I don't know, I will just answer both.
What makes me like a game:
The main thing that draws me into a game is the gameplay (obviously). If the game's play style is either so boring and repetitive or bad/unlikable (by me) that I can't make it more than an hour on it without needing a day or two of break, I will likely not finish it. I can't really pin down the individual nitpicks that really drive me off game-play wise, but here are a few. I do not like open world games for the most part since they usually spend more time developing the landscape and trying to cram enough content to fill it into said landscape that the content they did add is usually sub-par and repetitive at best. I am not big on games that hold your hand way too much (I'm looking at you and your 20 hour tutorial FFXIII), but at the same time I would like to know how my interactions affect the world I am a part of as well (I.E. story mainly). I can't stand back tracking, and if I have to do more than 5 hours of it over the entire course of a 40+ hour game, I'm done right then. Many many more here
I do not like it when the developers split up parts of the main story behind DLC's, Pre-Orders, Special Editions, Season Passes, and the like, and when that happens it tends to turn me off from the game before I even try it. That said, those I have tried I ended up liking until I noticed that I couldn't complete a quest they started in the main game because I don't own a DLC!
I can't handle repetitive combat! If I am expected to do more than 20% of my total played time in combat, the combat had better damn well be interesting and continue growing (adding techniques, skills, new enemies with new weaknesses, etc).
I really loathe games with way too much narrative. When I kill a boss, I don't want to be dumped into a 15 minute diatribe about your bad assedness or hear about how the boss used to be this really nice person who just lost it at one point and jumped into a vat of turn you into a psychotic bad ass or whatever. Just do what you need to get the point across and move on with the story. Besides, you should really be telling the story through the game anyway, not a series of videos after you kill each boss.
I can't stand quick time events (AKA: Press the series of buttons the game prompts you to or die because!). I'm not going into detail here, I just don't like it what-so-ever!
I do like games that tell a fun and engaging story through the gameplay and environment, I don't mind the occasional video of short to moderate length at most (5 minutes of solid cutscene is about my limit). I really like it when the story is so engaging that they can hide pieces of it and you have to explore to find out the unimportant details.
I prefer games with evolving gameplay. I don't mean that it starts as an RTS, turns into a Tactics turn based game, then to a JRPG, and suddenly a racing game out of nowhere. What I mean is the game keeps adding to the gameplay throughout the entire play length. I prefer it all to evolve the combat, the world, the story, the characters, and pretty much anything in the game.
I like it when devs know that player's are already used to a standard control scheme for most genres and don't try to re-invent the wheel every time they release a game, but at the same time I am always excited about new mechanics.
When game's don't let their previous entries determine what their following entries are going to be about. As long as it is still set in the same world or universe and the devs let you know that it isn't part of the same story as the previous, I am totally fine with it and often encourage it since it encourages fresh ideas in a stagnating industry.
Now for the other, what can impress me in a game I am playing that I already like:
When I have been playing it for more than 5 hours and didn't notice the time passing (especially if I have never played the game before), this absolutely astounds me and has only happened 4 or 5 times at most.
When a game suddenly kills off a main character and doesn't give you a way to take it back, provided it fits in the storyline and the way the character dies syncs up with the environment, characters, and atmosphere thus far.
When a game suddenly goes from almost about to stagnate to the point of me being bored (a death sentence for a game) to oh my god this is absolute amazingness! Why have I not experienced this before in this game? The best part is, it usually revolves around a feature or mechanic I thought I would hate and have therefor been avoiding it.
When a game manages to tell a complete story with character growth, plot twists (maybe, depending on genre), world growth, cause and effect, thorough structuring, good dialogue, great atmosphere, and most importantly a great plot line without needing to rely on cut scenes or long passages of text that pass for a loading screen between levels. This usually impresses me the most, particularly if they do it without cut scenes all together.
I could keep going all night, but my girlfriend tells me it is time to leave if we want to eat, so I must leave it short. Hopefully it helps you answer your question (whichever it may be).