The terrain spaces surrounding your City are called wildlands, and the rocky ones with some mountains on are called Hills. When hovering over them with the mouse pointer, it will give information about the benefit it will give you when you have conquered it. Clicking it will give information about current ownership and also give the possibility to scout it out or attack it.
Many players think that the hill of Rock Age is used to increase your stone production, but this is actually false. It is understandable though, as the hill does look like a mountain after all where you could get stone from. What the hill does is to actually increase your iron production by a certain percentage.
All wildlands increase your resource production apart from plains, which are valleys you can conquer and build new cities on.
All wildlands can be conquered and gatherred for gems except plains.
Scouting or attacking a wildland (without a city!) does not break the Beginner's Protection, even if it is currently owned by another player.
You get a better chance to gain Crystal, Agate and Jade by gathering in Hills. Like I said before, the percentage the valley will increase your resource production depends on the level of the wildland, but it can also vary between wildlands of the same level too. Number of troops and type of troops that defend each wildland also differs, but generally higher level wildlands have more and stronger troops.