There's actually three types of vision. This falls into the "line of sight" rules. The three categories are:
"Fog" - Places you have never seen. So you don't know what is there.
"Darkened" - Places you have seen previously but cannot see now.
"Light" - Places you can currently see because you do have line of sight to.
I don't know what the proper names are, but I use those names because that's what you actually see on the screen.
This can be confusing is because your cities have sight, your units have sight, but that your actual territory has "sight" too. So you can always see your territory and the hexes next door to it.
That means that how sight behaves when foreign units invade your territory is quite different to how it feels when you invade theirs.
If you are habitually a peaceful player staying mostly in your own territory, you won't get the feel of this. Next game, when you send your scout out exploring notice that once the scout is about 5 hexes away from the city there will be a darkened bit between what the scout can currently see and what the city can currently see.
It's actually quite realistic when you stop and think about it - it's just not the way computer games normally work....
EDIT: sorry, thought I should add that when an area is "darkened" you see only the terrain. Should an enemy unit move there you don't get to see it. It's realistic, why would your army know that the enemy is hiding on the far side of that hill if none of your units can currently see that side of the hill? If you just move blindly forward yes, you will sometime run into enemies that were there all along, but that you couldn't see. This is one of the better uses for horsemen - they can operate like battle scouts, move forward, find the units and retreat if necessary...