The BBC MicroComputer was created in 1981 by Acorn Computers Ltd with the collaboration of the BBC (BritishBroadcastingCorporation). The BbcMicro was common in UK schools in the 1980s; as a home machine, it was never as common as the CommodoreSixtyFour or ZxSpectrum?.
As it was more expensive, it was not quite as common as the two mentioned, but it had decent market share.
It had a 6502 processor, 32k of RAM, 32k of ROM, 7 different display modes and lots of interfaces (RS232/RS423, Parallel, 5.25in floppy, "1MHz bus", "Tube"... the "Tube" was for attaching extra processors) on the back for plugging in home-made devices. The CPU and the RAM ran at 2 MHz; the graphics chip ran at 1 MHz, accessing the RAM in alternate cycles with the CPU.
It had a built-in BASIC interpreter that was renowned to be the fastest of its kind. The BASIC interpreter included a nice assembler, and decent facilities for interfacing to code written using the assembler. The variant of BASIC (BbcBasic) was very advanced for its time, with features that were much closer to Pascal than the BASIC variants on other micro's. For example, you didn't need line numbers and could create named procedures with local variables.
One of the graphics modes, ModeSeven, was the same format as TeleText; it used very little memory (there was no screen bitmap - only the character grid was held in RAM, with the bitmap being generated on the fly by the graphics chip), and provided colours, flashing, and a double-height text facility (CHR$(141)!). Oh, and a set of "low-resolution graphics" characters, letting you effectively use this mode for graphics with a massive 80x75 resolution. :-)
The BbcMicro was rather similar to - but much improved from - the AcornAtom?; before the BBC came along, Acorn had been planning to release it as the "Proton". The Atom was also 6502-based and had a similar BASIC, but it had a slower processor, less memory, poorer graphics, no floating-point operations in its BASIC (unless, IIRC, you paid extra), and not as many handy interfaces.
A cut down version of the BbcMicro was the "Electron", which was closer to the price point of the C64 and Spectrum. Later BbcMicro models included the "BBC Master", which included 128K bank-switched RAM (if I remember right). The slightly later "Master Compact" model also came with a plinth, containing the machines' PSU as well as a floppy disk drive.
For some historical info, see http://bbc.nvg.org/history.php3 and http://www.mcmordie.co.uk/acornhistory/acornhistory.shtml.
See also AcornArchimedes, which was its successor.