The Clone Doctor was created as a result of regenerative energies present within The Doctor's severed hand.
When Donna Noble touched the casing of the severed Hand, it broke as it took in the Human DNA and created a Time Lord/Human hybrid that possessed one heart and aged as a Human did. The clone also contained parts of Donna's personality and mannerisms but mixed with his own intelligence.
The clone had caused the genocide of the Daleks, something the real Doctor disapproves, even when it comes to the Daleks. Because of this, he had to stay with Rose and Jackie Tyler in Pete's World, where Rose was to make him a better person, as she did when she first met the ninth incarnation.
The clone has a major flaw with being a Human/Time Lord hybrid; he only has one heart and can age and die without the ability to regenarate, so that he can literaly spend the rest of his life with Rose. He was the one that finally said he loved Rose and she kissed him.(DW: Journey's End)
Notes
The clothes that the Clone Doctor chooses reflects the proposed outfit Tennant was to wear in Season Three opener Smith And Jones, with the Doctor wearing a red t-shirt under his blue suit as opposed to the light blue shirt/tie combo that was eventually used. (DW: Smith and Jones (commentary))
