The TARDIS is the Doctor's transportation through all of time and space. It stands for "Time and Relative Dimension in Space."
It has a broken chameleon circuit which is why it is only seen in the form of a police call box. Another name, appointed by the Doctor, for this time machine is Sexy.
River is the Doctor's wife. She is the daughter of two of the Doctor's companions, Amy Pond and Rory Willams. Her birth name is Melody Pond.
River's main occupation is as an archeaologist, but she travels with the Doctor and her parents and is the only one that can make a Dalek beg for mercy.