TrueType is the font definition format used natively in Microsoft Windows and MacOS, and in other OSes via FreeType library and other implementations. It was originally designed by Apple. Sampo Kaasila was its principal inventor.
The project was originally named Bass - the fonts were supposed to be scalable and the fish has scales.
Apple originally used Adobe's Type 1 format, but it had limitations in hinting side. Type 1 could only have something-like-that hinting; TrueType, then, has a whole programming language to provide hinting at specified point size. Clearly much cooler than what Type1 can provide.
TrueType first appeared in Macintosh System 7 in 1990; Microsoft first provided it in Windows 3.1 in 1991.
Afterwards, TrueType became what is called these days OpenType - this was developed by Microsoft and Adobe.
Sources: "A Brief History of TrueType" in Microsoft website and some other sites that I couldn't remember anymore.