In the Wreck-It Ralph universe the word "Turbo" is used as a synonym for the word "crazy" but with slightly more meaning.

We can see this in multiple places throughout the film:

At the start, when Ralph is talking at the Bad-Anon meeting:

Satan - You're not going Turbo, are you?
Ralph - Turbo?! No, I'm not going Turbo!
Ralph - C'mon guys! Is it Turbo to want a friend?
Ralph - Or a medal? or a piece of pie every once in a while?
Ralph - Is it Turbo to want more out of life?

Later, when QBert is talking to Felix and Felix is translating:

Felix - Stand by, my QBertese is a little rusty.
Felix - Ralph's gone Turbo!!
Felix - Shining!

And again when King Candy is talking to Ralph:

King Candy - Bad guys don't win medals.
Ralph - Well, this one did!
Ralph - I earned it over in.. Hero's Duty.
King Candy - You game jumped? Ralph!
King Candy - You're not going Turbo, are you?
Ralph - What? No no no no..

From the transcript on springfieldspringfield.co.uk (now via web.archive).

So why don't the characters just use the word crazy?

Well they do, several times, however "Turbo" has additional connotations which make it more appropriate in certain contexts.

We learn the origin of the term around halfway into the film when Felix explains it to Sergeant Calhoun:

Turbo was a character in a racing game who became jealous of another game's success, attributing it to the reduction in popularity of his own game. As a result, he game jumped into the other game to try and rekindle his fame. Unfortunately players ended up reporting both his game and the one he jumped into as being broken which resulted in both games being unplugged.

This act was considered so bad that people started referring to it as "Going Turbo".

Using a person's name in place of an existing term for a given action is a fairly common trope and happens in real life as well when someone pulls off a particularity notable example of the given action, good or bad. If you haven't heard of it before, here is an example of "Pulling a Monica" from the TV program Friends (the episode The One With the 'Cuffs):

Particularly important to note is that when using a term as a substitute in this way, the actual act that takes place doesn't need to match the act that originated the term. So "Going Turbo" does not specifically mean "jumping into another game resulting in both games being shut down" but rather "acting in such a reckless way as to show extremely little regard for yourself and others" (or however else you would describe Turbo's actions). A lot of the other definitions on "Going Turbo" seem to overlook or ignore this (such as Wreck It Ralph Wiki or Disney Wiki).

Finally, some speculation on my part as to why this term was introduced...

By using the term "Turbo" rather than just saying "crazy" the film makers have a way to introduce the character Turbo to the viewer very early in the film, way before they need to provide any background or context for him. They can also use this term as a subtle reminder to the viewer of the character, and they do, mentioning it at the start, a quarter in and halfway in before the reveal in the third quarter. Keeping the term in the viewers mind helps make the big enemy reveal even bigger and helps the viewer understand just how heinous the characters view Turbo's actions.

To go Turbo means to ruin the facade of the game for the gamers and risk the game being shut down as its "out of order". Prior to the end of the movie, people going between games only happened after the arcade was closed, so obviously no gamers notice anything. Towards the end, Qbert's team joins in the Fix It Felix game, but it is done in a way that makes it seem like its just an additional feature of the game.

I believe that's the major difference. Remember, Turbo jumped to another game and would wreck the gamer's car in order to win the race for himself. And of course, later you see he messes with the Sugar Rush Speedway game's programming itself, though this isn't known to anyone and can't really be part of what "going turbo" means.

It's like in Mario Kart when you get the glowing upgrade and are able to go fast and crash through everything without taking damage