Keith, I started with an OM-1 as my first "serious" camera and always had a soft spot for Olympus. Like Konica, they were a smaller manufacturer with a deserved high reputation for quality optics. When they started a new, open-standard mount (original 4/3 mount) the idea was to create an open standard that allowed other manufacturers to produce bodies and lenses independently, complying with the open 4/3 standard. Panasonic was the only other manufacturer to take up the opportunity. Later on, CV started making lenses.
The promise of four-thirds was significantly smaller bodies and lenses than APS-C and full frame, while still delivering on IQ. Some loss of DOF was the price. The first Oly DSLR to earn a reputation with the new mount was the E-1 in 2003. It was fully weatherproofed and became much loved by nature photographers as it also had Oly's patented SSWF dust reduction. There were a few quality, read premium priced, lenses to match. However it wasn't a particularly compact camera, and the lenses weren't all that much smaller. Improvements in APS-C cameras and lenses brought out by competitors who had shorter product cycles left Oly sales languishing to the dedicated few. Oly's sensors were not able to compete with the "more megapixels are always better" mantra in the marketplace, even though their in-camera colour processing and jpg quality were always superb.
More trouble for the four-thirds format was the continuing shrinkage of APS-C dslrs, which from memory were physically no bigger and offered newer, higher resolution sensors with better high iso performance and wider lense choice, even if they weren't built to the quality of Oly's offerings. Four-thirds cameras started losing the battle for shelf space in camera stores, despite excellent cameras like the E620.
The only solution was to redesign the four-thirds mount to reduce the flange distance, enabling the design of more compact lenses and bodies while retaining the same sensor dimensions, allowing use of existing four-thirds lenses using an adaptor. Unlike four-thirds, micro four-thirds is not an open standard, but from what I can tell that hasn't made any difference.
There is big demand for small cameras with quality, compact interchangeable lenses that deliver on IQ - just like the original Barnacks and Ms. Micro four-thirds sales started taking off when Olympus and Panasonic started delivering on this promise - a promise that included a lens roadmap that featured fast primes in the most popular equivalent focal lengths. CV started making primes for micro four-thirds, followed by Zeiss. Relationships with Leica ensured continuing quality in the lens line-up. Panny's quality compact 40mm at an affordable price probably helped strengthen the format.
Panasonic also realised that micro four-thirds also allowed cinema quality video and shallow dof effects compared to existing camcorders. A new market in video emerged for the micro four-thirds mount. Why buy a RED when you can get great quality out of a hacked GH3. Things started to look good.
Other manufacturers saw the booming sales in micro four-thirds and quickly developed their own compact interchangeable lense cameras. Sony released the NEX cameras with APS-C sensors and very small form factors - apart from the lenses! But the crop factor for M-mount users was only 1.5 for the NEX compared to 2x for micro four-thirds. And Sony upped the ante with their EVF.
Olympus' response seems to have one-upped everyone with their new, very fast autofocus. That, and a new generation sensor that has excellent DR and high iso performance in the OM-D, along with a good EVF has put them back in the running. I sincerely hope they succeed after their corporate fiasco. With quality OEM and third party lenses, competitive bodies and IQ I think the format is here to stay. The wider lense choices are what gives the mount an advantage over Fuji.
If I've missed some stuff in this potted history, maybe others can fill in the gaps!
Some links:
http://www.olympus-global.com/en/corc/history/camera/digital_sref/index.html#04
http://en.wikipedia.org/wiki/Micro_Four_Thirds_system