Re-rolling is the term used when someone scraps all the progress they have made in a game and starts from the beginning. The term holds its roots in pen and paper RPGs where you literally roll dice when you are making a character to determine starting attributes. While re-rolling is still commonly associated with RPGs, the advent of persistent progression in a multitude of genres has started to see its use applied much more broadly.
Why we re-roll.
Re-rolling may seem strange to those who do not play games but I think it is perfectly understandable. Usually the first few hours of a game are some of the most interesting; the setting unfolds and the role you play within it becomes defined. It is during these early hours that you establish a feel for your character's strengths and weaknesses. In RPGs and online games, this is also the early stage where you might see what your character does in comparison to others. Sometimes it is possible to fall into the trap where seeing someone else do something that looks really cool makes you want to try it out yourself. Then, after starting from scratch and progressing a few hours again, something else catches your attention and the process repeats. I think what gets tapped here is a latent desire for exploration and to experience all the ways to play that can often be just as fun as moving the plot along.
Another reason for re-rolling is the pursuit of perfection. In RPGs this might be a feeling that a skill could be better allocated. For a stealth-based shooter it might be the need to complete a level without being detected. In either case, I suspect that each re-roll is in pursuit of the elusive 'perfect' play through. That is to say, the most optimal and flawless way to finish the game. In days of yore the perfect play trough was often a set of self-imposed rules (in these cases beating the game one way resulted in difference from beating it another), in modern times it is often dictated as the run that garners the most difficult achievement/trophy. The perfect play through isn't merely beating the game, it is an unraveling of its intricacies and secrets; more of a conquering of the game. I think the pursuit of perfection is something that we can all relate to on some level and it explains re-rolling quite a bit.
One final factor that I think contributes to the re-roll is comfort. When replaying a level that they are already familiar with, the player is comforted in knowing what is around each corner and what nasties to avoid. I think this is the same mentality as what makes a scary movie less scary the second time around and works to make a game less stressful. This point probably goes part and parcel with the above two. In order to best experience a new way to play the game it helps to have a reference point and in order to achieve perfection a bit of precognition can't hurt.
What's wrong with it?
The short answer to this question is that, if you are having fun, then absolutely nothing. Games are entertainment and however you achieve that is your own business (unless you are trolling and ruining someone else's good time; then you go burn). That said, I think that re-rolling does present some unique consequences that can severely limit one's impression of a game. For one, re-rolling cuts plot progression which isn't such a big deal if you are playing Call of Duty but becomes more of an issue in RPGs where plot is often one of the biggest selling points. For another, early stages of a game are often tuned in difficulty quite differently from later stages. In RPGs it is not uncommon for magic users to start off frail and relatively powerless to see them blossom into the most dominant forces in the late game. As such, re-rolling prohibits a player from seeing the best parts of the class. On this point, it also prohibits a player from experiencing the best challenges the game has to offer. Finally, early re-rolling might cause a player to miss out on the introduction of new game mechanics and thus, again, miss out on crucial gameplay elements. All told, the chief problems with re-rolling stem from preventing a player from fully experiencing a game if they don't break the cycle and fail to progress. For a developer, the re-roller presents an interesting conundrum; they may never see the later parts of your game but you want to try to design something that everyone in your audience will enjoy. Because of this, I think that some of the best designed games implement mechanics that mitigate the desire to re-roll or are, alternatively, built entirely around the concept of starting over.
Obviously one of the easiest ways to limit re-rolling is to provide less options to the player. If you have no customization options and the plot is completely linear then the player has little reason to start again. Mario is a classic example where a player has little incentive to start from the beginning unless they have hit the game--over screen and lost all of their lives. While this approach limits re-rolling, it can also severely hamper gameplay. Thus the difficulty rises in trying to find a solution that does not mitigate player choice but still discourages constantly starting from scratch. Trine is an excellent example of this. On its surface, it is a puzzle/action game set in a fantasy world with multiple classes. The twist here is that the player can switch between any of the classes at any time allowing the player to progressively explore while seeing all the bells and whistles of each class. Trine's switching mechanic even goes so far as tho be integral to solving most of the game's puzzles. Along these lines, the recently release Marvel Heroes featured a similar mechanic in that the player can switch between their heroes on the fly thus allowing for continuous plot progression without feeling the need to start again to try a different hero (that said Marvel Heroes is a terrible game overall for numerous other issues, but they at least got one mechanic right).
A counter option is to design mechanics to overtly encourage re-rolling. Faster Than Light is a game where you design your own spaceship and are basically presented with a continuous stream of choices (what crew do I recruit, what armaments do I load, etc.). The game is often punishingly difficult through random chance encounters and, as such, games rarely last long enough to hit the need to re-roll point before the main story finishes (if you make it that far to begin with!). All this assembled results in each game being unique and encourages players to experiment each time they play. In other words, the game is essentially built around the idea that you will die and that you should want to start again with a different approach next time.
Another good example of embracing the re-roll mentality is Spore. Getting to the late stages of the game is generally pretty easy and the design of the game is meant to encourage your unique alien creation. While there is theoretically an 'end' to the game, it is really more as a reward for the staunchly committed rather then a true goal to strive for. As such, it is strongly encouraged by the game to constantly start again and create a new species. Indeed, a lot of the fun in Spore can be found in the creature creator where, in playdough-like fashion, you can design your own abomination. The game overtly makes this a focus by actively encouraging users to upload their creations and share them with the rest of the world (a sort of meta-game to create the most fantastical or phallus-shaped creation).
In the end, I don't want to advocate how one should derive entertainment from their games but I think that re-rolling poses unique challenges for developers. Ultimately, games that either wholly embrace or mitigate the desire to re-roll are some of the best designed. Now to delete this post and start again...