Cobb was a general encountered by the Doctor, Donna (and later Martha) on the planet Messaline. He commanded Cline and the Doctor's daughter, Jenny.
Biography
When Cline captured the Doctor and Donna he took them see Cobb who assumed they, along with Jenny, were pacifists from the Eastern Zone.
Cobb asked the Doctor to join his army in the war against the alien Hath. He sought "the Source" and it was his mission to get it. He believed the Source would give him the power to kill every Hath on the planet. When the Doctor refused to help, and instead spoke of stopping him, Cobb had the Doctor and Donna arrested along with Jenny for not supporting him in the war.
Cobb found Cline tied up on the floor of the cell discovering that the three of them had broke out. Cline explained that Jenny had tricked him.
Cobb and his soldiers chased the Doctor, Donna and Jenny down into secret passageways uncovered by the Doctor. When Jennt tried to buy them some more time by holding up the soldiers she hesitated to kill Cobb. He tried to convince her to join his cause, stating that it was "in her blood." Jenny was already loyal to her father, the Doctor, and he had told her before that there was always a choice in whether yo kill someone or not. Instead hit a pipe to hold up Cobb and his troops. When the Doctor told Cobb that if the Source was a weapon he'd never let him have it Cobb threatens to kill him.
The Doctor, Donna and Jenny are reunited with Martha, and find the Source first. They discover it is a Terraforming device. The Doctor declares the war is over and releases the Terraforming device.
Cobb blamed the Doctor for taking away his chance of victory, and tried to shoot him. Jenny stood in the way to protect her father but Cobb shot her anyway. She was shot through one of her hearts and was (temporarily) killed.
Devastated and desiring revenge for Jenny's death, the Doctor held a gun to Cobb's head and contemplated killing him. The Doctor managed to stop himself, telling Cobb that "[He] never would" and that it is on that basis that the new society of Human and Hath should he founded. Cobb was demoted, arrested and imprisoned for Jenny's murder. (DW: The Doctor's Daughter)
Other information
The Human-Hath War is revealed to have only lasted seven days and that the myth created around the Source was the result of the generations from the progenation machines. It is not explained how while the other troops are all young adults whereas Cobb appears to be middle-aged, and yet still believes in the myths around the Source.
Russell T Davies suggested in the pod cast for the episode that, as well as creating a child from a parent, the machines were able to clone important figures. Therefore General Cobb could be the fifth Cobb of that week.
Behind the Scenes
Some fans have noticed that Cobb shares the same name as Jayne Cobb, a similarly thuggish character from another cult science fiction television series, Firefly.