.tiff, or Tagged Image File Format, is a raster interchange format that was originally designed to be a common format generated by scanners and used by printers.
It can support multiple color spaces, and even layers. However, the latter is a bit odd, as the official specs, owned by Adobe, have a different way of saving layers to tiff than Photoshop, also owned by Adobe.
As an interchange format, .tiff is not meant for sharing on the internet, and you will not find many websites that do accept it. However, printhouses know the file format, and will likely accept it.