The first computer worm to spread widely through the Internet in 1988 was the Morris worm.
This question concerns the historical significance of the program, rather than only its release date. The worm exploited vulnerabilities and weak configurations in several Unix services, including flaws associated with sendmail, fingerd, and rsh. It also tried to determine whether a machine was already infected, but its repeated-copy behavior caused more duplication than intended.
The early Internet was far smaller and less segmented than today’s global network. As a result, a program that moved among connected Unix hosts could spread rapidly and disrupt a substantial share of available systems. The event demonstrated that network connectivity could magnify a software mistake into a broad outage.
The Morris case influenced computer-security research, incident response, and legal policy. It also helped popularize the term “worm” for malware that propagates between computers without requiring a user to manually copy it.