The peak of Olympus film SLRs was in the OM family - OM-1, OM-2, OM-4. They were manual focus systems - body and lenses. When the film camera industry matured the other brands, Minolta, Nikon, Canon had manual focus SLRs and evolved or started scratch with autofocus systems - Olympus did not embrace that in volume - they did have the odd model but not mainstream. Thus, when the digital age arose, they decided to start completely from scratch.
They decided on a new digital sensor size - half the diagonal of 24mm x 36mm film (otherwise known as 35mm or Kodak 135) and an aspect ratio of 4:3. And their digital lenses were designed with the relevant smaller imaging circle. They called this the Four Thirds Standard. I think their reasoning at that time was that digital sensors were incredibly expensive and they wanted to reduce the costs. They believed that silicon technology would advance rapidly and the handicap of a smaller sensor would be overcome for reasonable photo image performance. Because Olympus is not as large a company as Canon and Nikon nor does it hold the duopoly's market share, they wanted this to be a new Standard, not a proprietary system so that they could get partners to come on board. Panasonic (with Leica) came on board for bodies and lenses, Kodak Digital provided early sensors but there were not many significant others. (By the way, Four Thirds refers to the 4/3 inch 4:3 ratio vidicon tube)
Although a bold initiative, Olympus and Panasonic suffered badly. For several reasons.
They failed to make the bodies and lenses significantly more compact than Canon / Nikon.
Sensor technology in those days was quite primitive - the smaller Four Thirds size meant that there were obvious handicaps in high ISO, dynamic range.
Autofocus technology in Four Thirds cameras was lagging behind that led by Canon / Nikon.
They could not establish volume sales and income to sustain their investment in high performance, ambitious, premium and pro lenses.
They failed to break into the Pro Photographer market in significant measure, so could not create the "halo" that would lead consumers in.
One thing that they innovated was Live View and auto focusing in Live View. But year after year, the venture brought financial losses.
They made the decision to step back from Four Thirds production. Using what they had learnt, they decided to create the Micro Four Thirds Standard.This would open up a new frontier, away from the dominance of Canon / Nikon. To do this, these cameras would be Mirrorless (avoid DSLR technology) - in this way, the camera bodies could be much more compact than a DSLR and since fast interchangeable lens autofocus without a mirror would be new territory, Canon / Nikon would have no superiority, in fact would have a handicap because of their vested interest in DSLRs with mirrors. As a second try, MFT finally made good in terms of sales income. The reasons for success are:
The sensor technology has improved to such a level that absolute high ISO performance for general use is more than acceptable, dynamic range is more than acceptable.
Autofocus technology for mirrorless bodies is acceptable for general use.
Bodies and lenses have been made even smaller in general. Some lenses are inevitably large and heavy but the buyer knows that those are ambitious high-performance designs.
Video making is now as important as shooting stills. For consumers, autofocus and sighting in mirrorless cameras are more convenient for video making.
There is sufficient inertia this platform is sustainable. Conversely, the market perceives that Canon / Nikon DSLR equipment is heavy, large and innovation has plateaued. Instead of the top line of DSLRs being "halo" products to entice people to the brand, they are perceived as not cost efficient.
The early Micro Four Thirds models from Olympus were aimed at a market niche where Canon / Nikon had no presence - female, small, life style aesthetic. They would progressively earn income while the technology improved and overcame handicaps. Panasonic relied on background in video production and aimed at semi-pro video makers as well as serious stills shooters. As the technology improved, Olympus moved from relying on the small PEN models to the more comprehensive OM-D models.
By the way the "Micro" in MFT does not refer to the sensor being smaller at all, it refers to the smaller lens mount.