The spinal cord is the extension of the central nervous sytem going downwards from the brain, beginning at the inferior end of the medulla oblongata at the foramen magnum in the skull and ending way down in the lower back. It consists of nerve cells and their axons, with white matter enveloping grey matter. It lies within the vertebral column, surrounded by cerebrospinal fluid. As with the other parts of the central nervous system, the spinal cord is wrapped in the meninges.
In the foetus, the spinal cord extends all the way down to the sacral vertebrae. As the person matures, the spinal cord shortens relative to the rest of the body, so at adulthood, the spinal cord only reaches up to around the level of L1 (the first lumbar vertebrae) where it terminates and the cauda equina begin - this is why lumbar punctures are usually carried out in the adult at the level of L3/L4.
The spinal cord develops in the foetus from the neural plate which folds to become the neural fold and then the neural tube before differentiating into the spinal cord proper.
The spinal cord carries sensory signals and motor innervation to most of the skeletal muscles in the body. Just about every voluntary muscle in the body below the head depends on the spinal cord for control. Similarly, most cutaneous sensation below the neck is transmitted via the spinal cord. Most of the sympathetic pathways and the lower (i.e. non-vagal) parasympathetic pathways also go through the spinal cord.
Damage to the spinal cord can result in paraplegia or quadriplegia, depending on the level of the spinal cord that the damage was done at.