The most complex group of animals to exist are the Chordates; comprising of all vertebrates and some invertebrates the Chordates all share and experience certain characteristics at some stage in their development.
These characteristics are what defines the chordates as complex animals. A notochord, the cartilage between the nerve chord and the spinal cord is only present in chordates. The dorsal hollow nerve chord will eventually develop into the central nervous system. Pharyngeal slits are gill like structures, we lose these before leaving the womb but some chordates keep them their whole lives. the final characteristic that defines and organism as part of the phyla chordata is a post anal tail. In humans, this is our coccyx.
Contain all of these characteristics and it’s safe to say you’re a complex Chordate.
From Crash Course: Biology on YouTube presented by Hank Green.