The genre of parking games encompasses a large assortment of games, ranging from slow-paced puzzle games to reflex-testing timed games. In the most basic puzzle-based type, this is an relatively classic type of game. It can be traced back to old-fashioned slider puzzles like "Traffic Jam" and "Gridlock", in which your task is to move blocks, or vehicles around until you get the vehicle to the target position. The modern variations vary from faithful implementations of these puzzles to what amount to scaled-down driving simulations.
In these puzzle-type parking games, as mentioned above, the goal is to figure out the sequence of moves required to get from the start to the end. Sometimes you will have multiple vehicles that need to be moved. It may be timed, either to set a limit on the time required to figure out the puzzle, or simply as a means of providing some measure of achievement more than simply completing the level. The level of realness can vary as well: Several games in this category are fairly accurate copies of the old block-and-slider games, while several involve a more realistic space for the player to travel in with more possible directions of movement. For the most part, in these puzzle-type car parking games, the player is in absolute control of what happens: the surroundings is static, and the main goal of the player is figure out the best sequence of movements to manipulate it.
In contrast, the other end of the spectrum consists of games in which the environment is not static, and the goal of the player is to respond to it. The original goal remains the same: get from some place to another. But now the goal is to respond to obstacles that show up along the way---generally other vehicles. These are frequently much more based on quick reaction time on the player's part, and planning at the beginning of the level are typically less useful. The key emphasis is on the player's ability to respond to either random or timed obstacles.
From the standpoint of a developer, the core mechanic of car parking games gives a lot of room for tweaking side-mechanics and themes. For example, one entrant into the field involves moving snow to a target with a plow while avoiding parked cars. Likewise, levels can a great deal be automatically generated pretty successfully, generating tremendous replay value. It is also ordinarily reasonably obvious what will make a difficult level and what will make a simple one, allowing for simple fine-tune of the difficulty level.
From the point of view of a player, parking games typically fall into the category of "difficult to master, easy to learn." Usually the primary goal and mechanics of a parking game are fairly intuitive, but a well-designed one can continue ramping up the difficulty level as well as tossing new curve balls at the player. As well, the range of games from puzzle-based to twitch-based means that parking games as a genre can appeal to a large range of casual and not-so-casual gamers.
Parking games are a somewhat new category of games, and there's plenty of unexplored territory. Happy gaming!