After you discover a hex, you can capture it. Capture lets you build, expand your faction territory, and earn sector points.
Capture is the transition of a hex under the control of your faction.
Capturing a hex is paid for with materia.
The price depends on the land, not on what is located on the hex.
Often you will see a message about insufficient influence. This is because contested territory can only be captured from the edge. Usually several hexes of your faction must be adjacent to capture such a hex; the exact number depends on the land or object type.
This rule often applies to fire, ice, sand, grass, and forest grass lands. Neutral and some special lands can be captured without surrounding them.
To defend the borders of your territory, build towers on the borders — the cost of destroying them is high, and this holds the enemy back. Try to keep your border dense: the more adjacent hexes your faction has, the harder it is for an enemy to push farther.
Once a month the discovered map shrinks from the outer edges. Capture helps you hold important places and avoid turning your territory into a long thin line.