A vertebrate is an organism that has a backbone.
Originally vertebrates only had a solid notochord. Modern vertebrates only have a notochord early in embryonic development, and this is then replaced by the segmented vertebrae. This allows for movement along the series of joints (created by the intervertebral disks). A few vertebrates actually retain the notochord into adulthood. So the definition of a vertebrate can really be a notochord (retained or lost in development), or a vertebral column.