Donna's World is the alternate universe created when Donna Noble turned left.
Alternate History
As the Doctor dies, various events set on contemporary Earth, go differently as he is unable to interween.
The Runaway Bride
The Doctor died while fighting the Racnoss, as Donna Noble wasn't there to stop him. UNIT declared him dead, dying too fast to regenerate. Rose Tyler meets Donna Noble for the first time. Donna Noble is later sacked from her PA job.
Smith and Jones and Series Three
With the exception of Oliver Morgenstern-- who survived as Martha Jones gave him her last piece of air--, all patients and staff of Royal Hope Hospital died of oxygen starvation. Sarah Jane and Luke Smith, Clyde Langer, Maria Jackson and Martha Jones were notable deaths.
The Doctor never met Martha, and therefore couldn't save the hospital. The events of The Lazarus Experiment and The Sound of Drums (the events of The Last of the Time Lords were negated during the Series 3 finale.)never happened, as the Doctor, Martha and Captain Jack Harkness never went to Utopia to remind Professor Yana that he was the Master. So the Mr Saxon regime could never have started.
The Voyage of the Damned
The previous Christmas's (DW: The Runaway Bride) events had gone differently so most Londers didn't flee the city, as they had in the "left" timeline. Wilfred Mott never meets the Doctor.
The SS Titanic, crashed and destroyed the whole city. Astrid Peth never met the Doctor, and was likely to have died during the crash. Most Londers, who notably didn't flee this year, all pershied. Notable exeptions include Wilfred Mott, Donna and Sylvia Noble; as Donna was told to go on holiday that Christmas, by Rose Tyler.
As London is destroyed, most of Southern England is infected with radiation. This displaces many residents of Southern England, including the Nobles. People were thrown out their houses for small things such as missing a single mortgage repayment, to make up for the lack of housing. The Nobles are moved into a house in Leeds, which they must share with other families.
Partners in Crime and The Sontaran Stratagem/The Poison Sky
America promise to financially help Britain, however sitautions arise over the Atlantic which makes them vulnerable aswell. For example, The March of the Adipose takes place there, instead of London. It is successful and many people die across different parts of the country.
As Britain is in such an unstable situation and other countries have closed their borders-- so deportation is out of the question-- they start sending "immigrants" to Labour camps. One of the families that get sent to one are living with the Nobles. Wilf, who served in World War II, is in horror. Seeing parallels between this and the Nazi regime which caused the Holocaust, saying that it had the same reasoning as "last time".
The ATMOS devices choke the world, they are shot down by UNIT in Britain. However it affects many other countries such as China alot worse. Since the Doctor, Martha and Donna never face the Sontarans, it's left to Torchwood members, Gwen Williams and Ianto Jones blow up the Tenth Sontaran Battle Fleet, sacrificing themselves in the process. Leaving Captain Jack Harkness distraught, and without a team. Rose remarks to Donna that they were the last ones left.
Negation
UNIT and Rose Tyler send Donna back to the time where the world split. Donna must make herself turn left. She runs out of time, and realises that the only way to change the timeline is if she is ran over, blocking her past self from driving round that way.