There are two ways to understand this question:
1) What makes us, humans, play games? 2) What makes games playable and enjoyable?
1) The first question is a question for the study of humans, namely cultural studies like anthropology. There is also the view of evolutionary biology, psychology or biology in general that can shed some light to the question by explaining play as a function for other purposes. Namely, this is one of the possible answers: function or for what other purpose does play exist. There are several possibilities, like maintaining social integrity, teaching small children about rules behavior etc.
There is also a danger in functional explanation. It has a habit of explaining away _phenomena. If anything _can have a function, then everything may have a function and there is only a short trip to everything having _a function. This is somewhat analogous to what Jesper Juul has said about games: games tend to be explained in terms of being something specific. (“Games are storytelling, games are how a child learn about rules.”) And there is a danger in this: if games are something, they can’t be something else. But they _might be something else, or a number of things.
Huizinga would have a ready answer to this question, and it would be something along the lines of play is what makes culture possible. He wrote the book Homo Ludens in order to express his view that play is a fundamental element of culture. That little word - of - is important. The translator named Homo Ludens ““A Study of the Play-Element In Culture” when Huizinga himself preferred “A Study of the Play-Element of Culture”. Bluntly put, culture is play.
2) This question can be understood in two ways: why are games enjoyable (assuming they are), and what makes a particular game enjoyable.
The first way of understanding the second question could be reformulated along the lines: why do humans enjoy play? This is almost analogous to the first question, but not quite. Commonly, the answer is that play is autotelic, causes flow or makes possible the attainment of other goals, like recognition.
The second way of understanding the second question is what bugs game designers. How can I make a game enjoyable and playable? I will try to answer this question (but I’m no game designer). This discussion is based partly on the book _Rules of Play _by Katie Salen and Eric Zimmerman.
A game should be elegant. This means both simple and easy to play. This doesn’t mean that modern games are bad because they are complex and contain lots of elements. It means that in order to achieve elegance, games should be as simple as possible without being too simple. This means that a game must manage to represent the thing it tries to represent. This isn’t as easy as it sounds, because this is very close to the definition of perfection: a thing is perfect if, when something is added or removed, it is degraded.
Each play should be unique. This isn’t exactly true. Every actual game has a limited number of iterations. What should be true that every occasion of play should be sufficiently different. Sufficiently, because games must escape excess repetition. To illustrate this, think about Chess. It has a limited amount of possible moves, but still every game manages to avoid overt repetition.
A game should offer interaction. This can be understood on two different levels, depending on what is meant with interaction. First, games should contain possibilities for contribution. If a player can’t affect the outcome, it isn’t a game. The first rule stands true also here: the amount of interaction must be sufficient. Second, (and this is a strong personal bias) interaction with other people makes a game better. Social games are more fun to play, regardless of the form of interaction. Multiplayer games are more fun even with mediated interaction.