Spotting is how you see other characters and armies in the game world. It is your most effective information gathering tool. Spotting is done both by your estates and your mobile army.
Two concepts come together for proper spotting. The spotting distance is how far from your position you can see, while visibility determines how easy an army is to spot.
Visibility is mainly based on the number of troops, but also on their type. Heavy troops in general are more easy to spot as they move slower, need waggons to carry heavy equipment and so on. Cavalry especially is easy to spot. In addition, visibility depends on the environment. In dense forests, it is easy to hide. In desert, scrub or grasslands, it is difficult to hide an army and it will be visible over a greater range.
Spotting distance has a base range and grows mostly with the number of scouts in the army. It also depends on the biome you are located in, same as visibility. Finally, if you are familiar with the region (see Region Familiarity under Travel), your scouts know where got spotting locations are, increasing your effective spotting distance.
To calculate who spots whom, both of these are taken into account. And yes that means a small army hiding in a forest will be able to spot a large army moving across grassland long before the other way around.
In general, the full spotting distance that is displayed both on the map and on your character status page is the distance at which you will spot a very large army. Half of that distance (also shown seperately on the map) is the distance at which you will spot a lone noble without army or entourage.
In addition to personal scouting, there are also watchtowers. Any watchtowers within your spotting range will automatically used by your scouts. Any watchtowers in the area of your estates will automatically be used by the local militia.
From those watchtowers, you will also get spotting alarms and characters spotted from them will be marked on your map.
Characters or armies inside a settlement have dramatically reduced visibility.
When your men spot someone, they will report what they have seen. These reports collect, so with a few spottings over some hours, you can draw a line on a map and make a guess where your target is travelling, for example. Your scouts will keep spotting alarms for some days to allow this.