“Weatherproofing” includes both “waterproof” and “fogproof”. “Waterproof” speaks for itself. The manufacturers have to make sure that no water/dampness enters the instrument at all, usually making use of “O”-rings. Sometimes the degree of “waterproof” is indicated by JIS-numbers (1-8), the higher numbers indicating the depth of immersion in water (e.g. “Waterproof up to 1 meter emersion for 1 minute”).
If the instrument is not properly waterproofed, dampness could also find their way into the instrument in cold, damp conditions, even though not directly exposed to water/rain. As the temperature drops sharply, the air inside the instrument is condensed, causing a lower than atmosphere pressure inside the instrument. Damp air from the outside is then drawn into the instrument, which condensates on the cold lens surfaces, rendering the binoculars useless. In the long run this eventually leads to the forming of fungi on the lenses as well.
Waterproofing will also prevent dust and dirt from finding their way into the instrument.
“Fogproof“: The only effective way preventing the instrument from fogging up inside in cold conditions, is to have the instrument “nitrogen-filled”. This way even the slightest bit of fog is removed from the instrument, making sure that no condensation of fog on lens surfaces is possible at all.