The Meta-Crisis Doctor was a Time Lord/human hybrid and a human incarnation of the Doctor, who possessed one heart, aged as humans did and had no regenerative ability to avoid death. He was created by an instantaneous biological meta crisis and was the final result of the Tenth Doctor's aborted regeneration.
However, this Doctor was born in a separate body than the original Doctor, existing as a separate person with DNA sampled from Donna Noble. These genetic alterations caused him to develop a unique, less merciful personality that deviated from the moral code that his counterpart followed. The new Doctor needed someone to look after him and quell the fire in his veins, and shared the same romantic feelings toward his companion Rose Tyler that the original Doctor could not accept as a slow-aging Time Lord. Thus, the Tenth Doctor made sure this version of himself would enjoy his life with Rose Tyler in Pete's World, fulfilling the need to make him a better person, and so his duplicate could give Rose the romantic life that she desired in his stead.
The Doctor's Hand
On Christmas 2006 in The Christmas Invasion, the newly-regenerated Tenth Doctor lost his hand in a sword fight against the Sycorax leader. Captain Jack Harkness later retrieved the hand and returned it to the Doctor in a jar in Utopia The Doctor's hand remained in the TARDIS until the Doctor was grazed by the blast from a Dalek gunstick, triggering his regeneration. After healing the damage to his body with the regeneration energy, in Journey's End, the Doctor channelled the excess energy into his hand, allowing him to heal without changing his appearance and personality. Even though the regeneration was aborted before it could be completed, the fact that the Doctor siphoned off the energy that would've changed his appearance after healing his injuries, he used up the same amount of regenerative energy as a full regeneration. This, as the Eleventh Doctor later told Clara Oswald, meant that his previous incarnation used up two regenerations due to "vanity issues."
Shortly after this aborted regeneration, the Daleks attempted to destroy the Doctor's TARDIS. Still inside the TARDIS during this apparent destruction, Donna Noble touched the energised hand's container. The regenerative energies present within the hand combined with Donna's human DNA, causing an instantaneous biological Meta Crisis. The force of the reaction shattered the container, allowing the energy to regenerate the entire missing body of the Doctor. In this process, the "Meta-Crisis Tenth Doctor" was created. He immediately dematerialised the TARDIS, saving it and Donna.
Genocide and Exile in Pete's World
After putting on a blue suit, the Doctor and Donna left the TARDIS and tried to attack Davros and the Daleks with his new weapon. Both were electrocuted by Davros. After the now-part-Time Lord Donna defeated the Daleks, she, the Meta-Crisis Doctor and the original Doctor teamed up to return all but one of the planets to their rightful places. The Meta-Crisis Doctor was then prompted by Dalek Caan to fulfil a prophecy by destroying the Daleks. He chose to do so and ignored pleas from both Davros and Donna. He proceeded to overload the Dalekanium power feeds, causing virtually the entire New Dalek Empire to explode, from individual Daleks to the Crucible itself.
Feeling his new, part-human counterpart was too dangerous to be left to his own devices, the Doctor entrusted him to Rose Tyler, taking the two of them back to Bad Wolf Bay in Pete's World. The Doctor told Rose that his part-human self needed her, that he was angry and vengeful as he himself had been when he first met Rose. He told her she had made him better, and now she had to do the same for his other, part-human self. Rose objected to this at first, insisting that the new Doctor was not really him, despite the Doctor's assurance that they were the same man and the part-human Doctor offering to spend the rest of his life with her. Rose asked both Doctors what the last thing they had said to her was when they were originally standing on Bad Wolf Bay. The Doctor was unable to give her a direct answer: "Does it need saying?" She posed the same question to the part-human Doctor, who whispered it in her ear.
Seemingly overcome with the revelation of his answer, Rose grabbed the lapels of the part-human Doctor and pulled him into a kiss, which he reciprocated. The Doctor looked on sadly yet stoically for a moment before returning with Donna to the TARDIS and leaving the parallel world. As the doors of the TARDIS slammed shut, Rose and the part-human Doctor broke from their kiss. The part-human Doctor took Rose's hand and watched the TARDIS dematerialise.
As a result of growing partially from Donna's DNA, the new Doctor inherited some of Donna's mannerisms. He claimed he had the same memories, thoughts and feelings of the original Doctor up to the point of his aborted regeneration, making them essentially the same man with physiological differences. However, the original Doctor was quick to point out that his new double was "born in battle, full of blood, anger and revenge". In this way, the Tenth Doctor described his duplicate as representing the way he had been during his former incarnation before meeting Rose. This motivated him to commit attempted genocide against the Daleks, an act the original Doctor condemned after the events of the Last Great Time War.