The operating system Steve Jobs brought to Apple through NeXT was NeXTSTEP.
Apple acquired NeXT in 1996, bringing Jobs and NeXT’s technology back to Apple. NeXTSTEP was a Unix-based operating system with an object-oriented software framework and development tools. Its architecture became the foundation for Apple’s next-generation operating-system strategy.
Apple developed the technology into Rhapsody and later Mac OS X, which launched for consumers in 2001. Mac OS X eventually became the basis for macOS and also influenced Apple’s other operating systems.
NeXTSTEP is sometimes confused with OpenStep. OpenStep was a related specification and software interface developed from NeXT’s technology, while NeXTSTEP was the operating system itself. The key historical connection is that Apple acquired NeXT partly for its software and engineering expertise, not merely for its hardware business.