First of all, you can see how to make a diagram here:
viewtopic.php?p=1693&f=5#p1693This makes it a bit easier to see what you mean

$$
$$--------------
$$|O O O O . . . . . .
$$|X X X O O O . . . .
$$|. . X X X O O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|X X X X X O O . . .
$$|O O O O O O . . . .
$$|. . . . . . . . . .
$$|. . . . . . . . . .
$$|
- Click Here To Show Diagram Code
[go]$$
$$--------------
$$|O O O O . . . . . .
$$|X X X O O O . . . .
$$|. . X X X O O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|. . . . X X O . . .
$$|X X X X X O O . . .
$$|O O O O O O . . . .
$$|. . . . . . . . . .
$$|. . . . . . . . . .
$$|[/go]
Black (X) and White (O) surround each other. Does this territory belong to black or to white, or does it need to be played out to decide who's territory it belongs to?
If it needs to be fought out, then why do opponents not always invade each other's territories to try and create eyes all the time. Why are territories ever left without a fight once they are surrounded. I have seen many games where I think I would continue fighting, but more experienced players don't?
Black is the one surrounding empty territory, so it belongs to black unless white can either:
a) create a living group in the empty area or
b) kill the black stones.
For white to create a living group, i.e., one with two eyes, inside that enclosed space is highly improbable because there is just not much room for him to do so and it should be fairly easy for black to prevent white from getting two eyes.
However, it is possible to imagine a situation in which white invades, black tries to kill him, but in the process removes too many of his own liberties resulting in either his death or a seki (where putting one's opponent in atari would put oneself in atari).
If white thinks he might have a chance at killing or getting a seki (in which neither player would get points in the enclosed area) he is welcome to try, and indeed a beginner can learn a lot by trying. More experienced players however recognize from their experience and their ability to read out a position whether an invasion is futile, so they don't bother.
Here, if white can prevent black from forming two eyes, he might have a shot. If you can't read that it's impossible, bombs away! Likewise for black - if he thinks white has a chance, he might prevent it by tossing in another stone for protection - but that makes his territory one point smaller, and if the invasion was doomed from the start and he loses the game by that one point, that will have been a big mistake!
P.S. Welcome to the forum!
Patience, grasshopper.