These figures denote the focal length of the lens ( what is commonly perceived as the optical power of the lens) and also the maximum aperture or speed of he lens
( this is the widest open that lens can go to let the light in)
For instance with this camera the lens is stamped 6.1 –30.5 mm 1:2.8–4.4
So the widest angle of view ( wide angle) is 6.1mm and the tightest angle of view ( telephoto) is 30.5mm. This mm size optically relates to the physical size of the CCD or in the case of a film camera the format of the film.
to 28 to 140 millimeters in 35mm) so the physical size of the sensor is smaller
than a piece of 35mm film
The figure 1: relates to the magnification and means that as long as the enlargement is not greater than one to one( that is the object does not project onto the ccd larger than life size the aperture figure will be true). With compact camera that have a set lens this has no relevance.
The figures following this 2.8–4.4 relate to the aperture, When the lens is set on wide angle - 6,1mm the widest aperture is 2.8, However as we zoom the optics alter and consequently the aperture shifts so that at the narrowest angle of view ( zoomed in to full telephoto ) the widest aperture is now 4.5.
So a lens that is 1:2 is faster and has the potential to let more light in than a lens 1:2.8
Because many people understand the focal length of a lens in relationship to a 35mm film camera this is often equated -
so the 6,1mm 30.5 mm lens is - 28mm - 140mm in terms of similar angle of view when using a 35mm film camera equivalent.