From Diablo Wiki
Rushing or turboing is the process of using a higher level character to assist one or more low level characters in a very speedy pass through the game. This sort of rushing can be subtle, such as giving a character a waypoint or killing a boss for them; or a full on safari guide style shepherding through entire acts or difficulty levels.
Rushing is done for various reasons; to rapidly level up new characters via experience exploits, to advance new characters to a higher level for a specific quest reward (rushing for runes from the Nightmare and Hell difficulty Hellforge quest was a popular pastime in Diablo 2), to power up a low level character (with quest rewards) so they'll be stronger for low level dueling, or just for fun.
D3 Team Approves of Rushing
The Diablo 3 developers do not want rushing to be abused, but they recognize that it's a social activity and something most players start to do once they've played other characters and experienced the early game content. Bashiok detailed their attitude in a forum post from April 2011.
Outfitting a new character with better items and having a friend with a high level character rush you through content, we’re totally fine with. While, yes, we could be sentimental and hope that you’re really interesting in experiencing the content at the pace and balance we worked hard to achieve, having a friend rush you through content is a positive social experience. Having them help you hit a level where you’re both able to tackle content that’s relevant creates a positive social experience. Regardless of the intended pace, it’s co-operative play, and that’s not bad.
Rushing through use of unintended mechanics or bugs to skip content is not something we’ll support, of course, and ideally we’ll fix any such issues should they crop up.
For example, it might take an hour or two to rush a low level character up to a higher difficulty level, and after an hour or two of play time there (sharing the experience of the kills made by other players) the low level character would have advanced to a high level that would have required many hours or days of play to reach normally.
It's common for low level characters to offer to give up the item drops or various quest rewards, in exchange for being rushed. It's very poor form to renege on this sort of agreement, but in the cut throat world of online gaming, it's not unheard of.
Rushing in Diablo II
Rushing is very common in Diablo II, since the shared experience at higher levels is vastly greater than what any low level character could earn playing for real. Also, many eventually grow bored of running through all of the quests and killing all the low level enemies. Players want to jump right to the end game, where the best items are found.
There is also a variety of nice quest rewards that characters obtain along the way. Rushing low level characters through of Nightmare and Hell in order to obtain the drops became a very popular past time once the quality of those runes was increased in the v1.10 patch.
Most games have various limitations imposed to stop or limit rushing. Examples include disallowing low level characters to share high level character's experience points, level requirements to pass certain quests or activating certain waypoints, etc.
Game developers generally try to limit rushing to keep it from being so easy that no one plays the early levels of a game, but they realize that players will eventually want to hurry through some parts of the game, so they don't stick minimum level requirements on every area or act.