Unlike most systems, IBM created an entire line of computers (or CPUs) from small to large, all running the same command set. This allowed the customers to use a low-cost version of the family, and upgrade to larger systems if their needs grew. Some models (e.g., the 360/30) even offered the option of microcode emulation of the customer's previous computer (e.g., the IBM 1401, or the IBM 1620) so that old programs could still be run on the new machine.
This flexibility greatly lowered barriers to entry. With other machines you had the choice between being able to afford a machine that might not have the power you needed, or instead purchasing one that guaranteed the power but cost so much to be unattractive. The result was that many companies simply didn't buy computers. The S/360 changed the entire nature of the market, and companies could now buy "low end" machines without fear.
The S/360 family initially consisted of six computers and forty common peripherals, there were thirteen models in all. The cheapest model was the 360/20 with 24k of memory, only half the registers of other models and the instruction set was not binary-compatible with the rest of the range. The most significant model was the 360/67 (first shipped in August 1966), which was the first to offer virtual machine computing to its users through its CP-67 operating system, later called VM/370 (see: CMS/VM).
Operating System/360 (OS/360) was developed for mid-range System/360. The smaller machines used DOS/360 and the larger were supposed to use TSS/360 (Time-Sharing System, a Multics copy), but it never worked properly and was replaced with either CP-67, MTS (Michigan Time-Sharing System), TSO (Time-Sharing Option for OS/360) or a number of others.
The System/360 introduced a number of the standards for the industry, such as 8-bit bytes (although there was financial pressure during development to reduce the byte to 4 or 6 bits!) and byte addressable memory, 32-bit words, segmented and paged memory, the EBCDIC character set and was the first to use microcode.
The S/360 was the most expensive CPU project in history. The most expensive project of the 1960s was Project Apollo moon rocket. IBM System/360 was the second most expensive. Fortune magazine at the time referred to it as IBM's '$5 Billion gamble' and they were right; IBM absolutely bet the company on this machine - that's $5bn *1964* Dollars! The bet paid off...
See also List of IBM products.