You have a 4 part question:
1) What the mm means?
The mm (milimeters) is a theorical distance from a point of the lens to the sensor (or film) plane.
Imagine a pinhole camera obscura. The distance from this pinhole to the back wall is the focal distance (A), which eventually defines the viewing angle (F).
If you increase that distance (B) the angle of view is modified acordingly (G).
In a pinhole camera the distance is exactly that, a phisical distance. On a glass lens this distance could not be exactly that becouse lens design, components etc. That is why I mention theorical.
1a) 35mm equivalent
Do not confuse this 35mm with the previous one. On this case the most widley used camera were the 35mm film (phisical dimension of the wide part of the film) As this were the most popular, when the sensor is of a diferent dimension is common to define the angle of view as an equivalent to the 35mm film.
In this case for example a 80mm lens could be equivalent in terms of the field of view on a big sensor or 15mm on a small sensor (F) remains the same.
2) Diferent costs
Some things to consider that defines diferent costs on a same mm size lens are:
Glass quality. Some low quality have can produce dispersion, or chromathic aberrations.
Number of elements Depending on the design, a "lens" can have diferent internal lenses to correct the light and give a better image.
Max aperture The bigger the aperture the bigger the glass needed.
Aditional things Like coatings, electronics, weather sealings, structural matherials etc.
There are several factors than define a lens size. A denser glass refracts light more than a low density one. This means that the low density needs more distance to focus than the denser one for example.
Lens elements, distances inside, etc.
Inclusive some large telephoto lenses can be Reflective rather than Refractive, so they use internal mirrors to bounce the light inside and shorten the overall length of the lens.
When a lens has a range (for example 70-300 mm) this means that has internal elements than can move back and foward and modify this focal length, therefore the field of view.
Between this theorical lenses: 55mm-200mm or a 55mm-600mm The biggest number means a more powerfull telephoto. So a far object will look bigger.