Optical format is the size of the sensor's active area, written as a leftover from old tube cameras. "1/2.8 inch" is not the diagonal in inches you can measure with a ruler. It is a name. The useful fact is the actual width, height, and diagonal in millimetres, because that is what the lens must cover.

In one sentence. Format is the size of the chessboard. It tells you which lenses can cover it, and what field of view a given focal length will really give you.
Why the inch number is a nickname
Vidicon tubes were sold by the glass outer diameter. The usable target was smaller. CMOS inherited the nicknames and not the glass. A 1/2.8" sensor is not 25.4 divided by 2.8. If you need the millimetres, read the datasheet diagonal, or compute them from pixel size times the pixel counts.
On Camemaker, the Optical Format filter is still the right first cut. It groups parts the way lens makers group image circles. Just do not convert the label with a ruler and call it engineering.
What format decides
- Which lens can sit in front. Image circle must be larger than the sensor diagonal, with a little to spare.
- Field of view for a given EFL. The same 4 mm lens is wide on 1/2.8" and tighter on 1/1.8".
- How hard the pixel has to work. Cram 12 MP onto a small format and each well shrinks.

A kitchen-table test
Cut two paper rectangles, one the size of a postage stamp, one the size of a matchbox. Hold the same drinking glass over each, as if the glass were the lens. The stamp sits inside the circle. The matchbox does not. That is 1/4" versus 1/1.7" behind the same M12.
People then ask why their "same 2.8 mm lens" looks narrower on the new camera. They changed the paper, not the glass.
How to read it on Camemaker
Filter sensors by optical format once you know the lens family you can afford (M12 on 1/2.8" is a different world from C-mount on 1"). Then open lenses and keep image circles that cover that format. If both sides only list the inch nickname, treat coverage as a question until the millimetres are in front of you.
Do not pick a sensor for megapixels and only then ask which format it is. That is how you buy a chip no honest M12 can cover.