The Dream Lord was a psychic manifestation of the darker parts of the Doctor's character, given life by psychic pollen that was stuck in the time rotor of the TARDIS. Due to his nature of being created from a mind, the Dream Lord had the ability to control the dreams of others as he wished, even allowing the Doctor, Amy and Rory to share the same dream. However he had, as the Eleventh Doctor put it, "no power over the real world."
The Dream Lord was "awoken" by specks of psychic pollen from the Candle Meadows of Karass Don Slava that had become stuck in the time rotor of the Doctor's TARDIS console. This pollen induced a collective dream state for the Eleventh Doctor and his companions, Amy Pond and Rory Williams, when warmed. The Dream Lord trapped the Doctor, Amy, and Rory between two worlds, one in a seemingly idyllic Upper Leadworth, five years in Amy and Rory's personal futures, and the other in a TARDIS hurtling toward a "cold star". He told them one of these worlds was a dream and the other was real. In each world, the three were to face "a deadly danger", and dying in the dream world would allow them to wake up in reality. In actuality, the Dream Lord had created both worlds; all the while they remained asleep in the Doctor's TARDIS.
The Dream Lord appeared to the Doctor and his companions in both worlds, taunting the Doctor on his insecurities and defects, and pressuring Amy to assess her own priorities and "dreams" for the future – whether she wanted a life of adventure with the Doctor, or to be settled safely with Rory and a family. He seemed to relish baiting the Doctor and his companions with remarks about their relationships. The Doctor recognised who the Dream Lord was because, in his own words, only one person in the Universe could hate him that much.
After they all died in the Upper Leadworth world, they were freed from the "cold star" by the Dream Lord as "reward" for apparently solving his puzzle. The Doctor then realised that neither world was real, and returned them all to the waking world by destroying the TARDIS and seemingly killing himself, Amy, and Rory.
Whether or not the Dream Lord was truly defeated was open for interpretation. After he had found and removed the psychic pollen, the Doctor saw the Dream Lord's face in his reflection in the TARDIS' console, smiling slyly at him. Being a representation of the Doctor's inner darkness, the Dream Lord may never be truly defeated, but only hiding within him. (TV: Amy's Choice)
The Dream Lord drew his personality and observations from the "dark" aspects of the Doctor's subconscious. This included his innermost thoughts and doubts about the course of his life and perhaps cavalier treatment of others, including self-loathing, guilt, arrogance, selfishness and even lust. The Doctor said to the Dream Lord, not long after they met, that he knew who the Dream Lord really was because only one person hated the Doctor as much as the Dream Lord did. An additional layer to the Dream Lord's identity emerged when the Doctor described the psychic pollen which created the Dream Lord as a "mind parasite". He also enjoyed making fun of Rory and his lack of common sense, something the Doctor was more subtle about. (TV: Amy's Choice)
Physically, the Dream Lord appeared as a short, older man. When he faced the Eleventh Doctor and his companions, the Dream Lord's appearance was generally a parody of the Doctor himself, (being a psychic manifestation of him) consisting of a tweed jacket, striped shirt and bow-tie strikingly similar to the Doctor's. He frequently changed his clothes to make fun of whatever situation the trio was in.