The roots of the term are traced back to early ways of printed circuit board design, when the enlarged (for higher precision) "artwork" of PCBs was manually "taped out" of tape and adhesive-covered PCB footprints on sheets of PET film. Subsequently the artwork was photographically reduced. The same used to be done for early integrated circuits. .
The term more currently also refers to the writing of the magnetic tape with the final data file describing the circuit layout and other details.
A modern IC has to go through a long and complex design process before it is ready for tape-out. Many of the steps along the way utilize software tools collectively known as electronic design automation. Tape-out is usually a cause for celebration by everyone who worked on the project, followed by eager anticipation of an actual product returning from the manufacturing facility (semiconductor foundry).
A tapeout is not always the very last point in the design of a new chip at the design house. The following things may happen.