The term BIOS originated with CP/M back in the 1970's but it is mostly associated with the IBM PC (1981) and its various clones and successors.
The BIOS gets control when the computer first starts up, via the reset vector of the processor at f000h:ffffh (or is rebooted using the Ctrl-Alt-Del key combination).
The BIOS then does a POST (Power On Self Test) which verifies the processor, various peripherals such as DMA, interrupt controller, and main memory are okay, and that there is a keyboard present.
In the original IBM PC there were no floppy disks, so the BIOS provided routines to interface with a cassette drive. A year or so later, floppy disks were added and the BIOS was upgraded to provide various functions such as formatting a disk, reading and writing sectors, etc.
Once the POST was finished, the BIOS would use its own disk routines to read in the first sector of the disk which contains the boot code -- this is then used to load in the operating system (e.g. MS-DOS, and later Windows).
Once MS-DOS was loaded in, the BIOS provided functions to interface with the video display, disk drives, serial ports, printer ports, keyboard, and real-time clock and other hardware. The interface was done via software interrupts -- for example, INT 10h was used for video, and INT 13h was used for floppy disk services.
Later, routines were added to detect PS/2 keyboards and mice, and still later, USB keyboards and mice during boot-up. Likewise, the floppy disk routines were enhanced to interface hard drives, then CD/DVD drives, and finally USB flash drives as boot options.
The original 16-bit versions of Windows (which essentially sat on top of MS-DOS) also made use of BIOS services. 32-bit versions of Windows have their own I/O routines and do not use BIOS services.
So by the definition of the BIOS given above, this is not really a OS, but just I/O routines which provide services to an OS (hence the name Basic Input/Output System). To have a minimal disk OS, you would need to add a file system and the ability to run programs off of disk. (The command line interpreter would be loaded off of disk when the OS starts up.) These functions could be included in the BIOS, but it is better to keep it as minimal as possible.