I participate in several third party Olympus and Micro Four Thirds forums.
And have friends who become Micro Four Thirds owners. So it is inevitable that I encounter newcomers to Olympus (although they may not be newcomers to owning DSLRs, SLRs or photography). I will endeavour to write this introduction with a balanced viewpoint and hope this helps newcomers.
Olympus has an odd way of naming their models. Marketing wise, they want to draw on their film camera history for nostalgia and owner fervour. Olympus made several film models that were legendary. The Olympus PEN-F half frame SLR and the Olympus OM 1, 2 and 4 family. When they made their digital cameras, they decided to leverage off the nostalgia associated with those names and came up with the family names PEN Digital and OM-Digital (OM-D). THERE IS NO NEED to call your camera OM-D E-M5, you can save time and effort in typing as well as comprehending by just typing E-M5. There are now follow up models e.g. E-M5 Mark 2 (the original is named E-M5 Mark 1 or simply E-M5) so be careful to mention whether your model is a Mark 1 or Mark 2. The worst thing you can do for comprehension is to call your camera OM-D E-5 or E-5. Because there is actually an old digital camera named E-System E-5.
The initial Olympus digital interchangeable lens cameras were DSLRs. They were called Four Thirds DSLRS. After that failed to be sustainable, Olympus made Micro Four Thirds mirrorless cameras. By the way the "Micro" in MFT refers to the smaller lens mount - the sensor in Micro Four Thirds is the same as Four Thirds. (For more information see Olympus Cameras - Before and Now
All Micro Four Thirds (MFT) lenses fit MFT bodies. That means Pansonic MFT lenses will fit and work with Olympus MFT bodies. And vice versa.
Four Thirds lenses can fit MFT bodies if you use electronically coupled adapters. The Olympus adapters are MMF-1, 2 and 3. The MMF-3 has seals that make it weather resistant. However, only the E-M1 sub family - the Mark 1 and the Mark 2 will autofocus at a reasonable speed with FT lenses. The other Panasonic and Olympus MFT bodies will ultimately autofocus a FT lens but it could take one or more seconds.
Panasonic lenses often have Image Stabilisation in the lens. Only a few Olympus lenses have that feature. Specific Panasonic body+lens and Olympus body+lens combinations enjoy synergistic Image Stabilisation - having unmatched body and lens combinations require you to switch to body only vs lens only Image Stabilisation.
MFT lenses were probably the first to store lens correction parameters in lens firmware - e.g. curvilinear distortion, vignetting corrections. Panasonic added chromatic aberration parameters. Until recently, Olympus bodies read and corrected curvilinear distortion and vignetting only.
MFT has a 2x crop factor in reference to "full frame" 35mm sensors. This manifests itself in that a 25mm lens from a film or digital "full frame" body will have a viewing angle similar to a 50mm lens on an MFT body.
You can fit legacy film or modern "made for digital" lenses onto MFT bodies using the relevant non electronically coupled, glassless adapter. Recently adapters with glass (first started by Metabones and later followed by Zhonyi) now allow optical compensation so that the crop is lessened by a factor of 0.7. At the same, the brightness of the combination is increased by 1 f/stop.. The adapters are generally not electronically equipped. Preferably the alien lens needs to have an f/no ring.
Olympus bodies usually have a magnification feature as focus assist. Newer bodies have focus peaking display. For MFT and FT lenses, the camera body knows you have touched the focus ring of the lens so either magnification or focus peaking or both can activate when you turn the focus ring. For alien lenses, no electronic signalling happens so you have to assign Fn buttons on the body to activate or de-activate these features,