"Despite criticism, the term gameplay has gained acceptance in popular gaming nomenclature, being the only common phrase describing story quality, ease of play, and overall desirability of a game all in one word." - Wikipedia
Wow, what a complicated way to define something so simple. In my opinion, Gameplay is simply the way the user play a game. The way the user scores points, how we progress through the levels, how we accomplish our goals and overcome our obstacles in the game.
Gameplay is important, really important in fact. Computer games are interactive, and gameplay is essentially the definition of the game's interactivity, how the user plays the game. For example, the game has a story and characters, which puts the user in a certain situation trying to achieve a certain goal. How the user achieves that goal is down to the gameplay. So it could be a first person shooter game where the user needs to shoot a bad guy. The 'gameplay' as such would define the actions needed to be taken by the player, to achieve that goal. So in this example the player would most likely need to shoot the bad guy. This is the gameplay, how the user 'plays the game'.
It is so important to get this aspect of the game right, you can have awe inspiring visual effects, a compelling story, but if the game is unwieldy, boring and repetitive, people wont like it. The gameplay of a game, is basically the core mechanics. Take Pac-man for example, you could put any story or graphics you wanted into the game, and it fundamentally wouldn't change, and chances are it would still be fun. This is because when pac-man was made, computers didn't have the space or power to rely on graphics or storyline, so games were essentially bare bones and gameplay oriented. Most modern games are just adaptations of old games, gameplay wise. 'Crysis' for example, is not a world away from 'Doom', same as 'Doom' is not a world away from 'Wolfenstein 3d'.
While the gameplay of most games is often copied and adapted, it still does vary quite a bit. Different types of Gameplay have different types of rules, but not all are similar. For example, 'Pong' has much different rules to 'Pac-man'. But no singular set of rules can encompass all types of gameplay, which is why it is important to make sure of good gameplay in a game when developing it.
Gameplay is generally defined by the game designers before main development of a game starts. When designing a game the concept artists are generally left to decide the look of the game, and the designers to figure out the mechanics, such as Gameplay. Gameplay is generally decided before a game is put into development and therefore is usually the basis for the rest of the design. Often a theme for a game can be chosen for the gameplay, but the gameplay is often the most important aspect of the game from an early development stage.