Final answer:
The development of the notochord is the major characteristic that emerged with the phylum Chordata, after the multi-celled life of organisms like jellyfish.
Step-by-step explanation:
The major characteristic that occurred between the multi-celled life of the jellyfish and the phylum "Chordata" is the development of the notochord. This feature is one of the key distinctions of the Chordata phylum and is present at least during some stage of development in all its members, which includes both invertebrates like tunicates and lancelets, and vertebrates. In vertebrate development, the notochord typically contributes to the structure of the intervertebral discs in adults, being replaced by the vertebral column.
Certain Chordata traits, such as the dorsal hollow nerve cord and the pharyngeal slits, contribute to the anatomy of the central nervous system and respiratory system, respectively. However, the presence and persistence of the notochord during some stage of development is what fundamentally distinguishes chordates from earlier multi-celled organisms like jellyfish which do not possess this structure.