Bainite is a structure which can form in steels, named after Edgar Bain (photo below) who discovered (with E. C. Davenport) the structure around 1930. This microstructure generally forms as an aggregate of ferrite (the stable crystal structure of pure iron at room temperature) and cementite/ carbides (stoichmetric combinations of iron, other metallic elements and carbon).
The components in the final microstructure can be similar to those forming at higher temperature in the transformation to pearlite, or upon tempering martensitic steels. The bainite transformation has different kinetics and transformation mechanism than pearlite or martensite, although all the details of the transformation are yet to be revealed and agreed upon. Bain reported that the microstructure appeared as martensite which had been subsequently heated to precipitate carbides, later work has confirmed that the transformation mechanism is martensitic (although most aspects are refuted by somebody).
Some bainitic steels are alloyed in such a way that the transformation occurs without the formation of any carbides. It is these steels which have been the topic of my own research.