Final Fantasy XIII is (by concept) to a large degree a strictly linear game. Most of the time (with the exceptions given below), the levels are a simple "tunnel" with no forks. You will only be able to stray off the path for some meters to find hidden treasure spheres or optional enemies. There are no side-quests in the traditional sense and you will only follow your main objective. Once you leave a level, you will not be able to return to the previous visited stages. This is a large departure from the gameplay of earlier parts of the series (say, FFVII).
On the plus side, the graphical representation and the atmosphere/mood of these tunnel levels is awesome. In fact, if you switch off the minimap you may even forget the limited topolgy and enjoy the surroundings. Also, the game uses the restricted degree of freedom for its intense and fast paced storytelling.
The exception from this rule come only very late in the game. FFXIII consists of 13 chapters. Once you reach Chapter 11, you will have access to a number of non-tunnel levels where you may roam freely, that is, as far as you can beat the enemies that stand in your way. Also, a number of simple hunting missions becomes available, where the simplicity refers to the structure of the quests and by no means to the challenge of the enemies. In fact, at this stage you are not expected by the game to be able to complete all challenges of Chapter 11. Rather, you should complete some easy hunting missions and move on with the storyline to level up. That is, you leave Chapter 11 to beat another sequence of tunnel levels in Chapter 12 and the final boss fight in Chapter 13.
However, from Chapter 13 (and even after finishing the final boss), you will be able to travel back to Chapter 11 as often as desired to beat as many optional quests as you like. This is intended as some kind of open-ended-like gameplay where you can find the characters ultimate weapons and fight some really impressive special enemies.
Personally, I really enjoyed the game yet I would have like a more open world. The story was exciting and was presented like an intense and fast-paced action movie. Yet, it doesn't reach the quality of earlier great storylines (like VII, VIII, or X). However, the real strength of the game lies in the combat system, which is strange at first, but works out great once you get used to it. I recommend to give this game a chance.