Even insects are capable of understanding this simple need. I have kept a mantis (stagnomantis limbata) in a fishbowl before, And after a few weeks, I could tell that she was desperate to get out. She'd wander aimlessly around the confined quarters and claw her way toward the opening every few minutes. Mantids naturally feel the need to roam and move around. She was so energetic when I finally set her free.
More "advanced" animals like chickens feel the same urge. Chickens confined to battery cages often are unable to unfurl their wings and are forced to sleep in their own fecal matter. They can barely move and often have something wrong with their legs. You can tell just by looking at them that they want out.
For those of you who've seen animals at the zoo, They have gotten used to the size of their enclosures. Similar to a criminal sitting in jail, They will at first struggle with the restricted space but will eventually stop fighting to get out. Does this mean they don't want to be free anymore? Of course not. I have seen a sow who'd been released from a battery pen onto a farm where she could live the rest of her life. As soon as she was released from the back of the truck, She immediately ran out and began prancing around on the grass and squealing and kicking her legs. If you think that animals don't have the capacity to understand freedom, Then I'm not sure how else to describe the sow. I could tell she was happy.
Animals most definitely understand the idea of being set free, but it is not the same way we perceive and define freedom to be. "Freedom" is a relative idea/concept. We all have different ideas of freedom, animals are no different. Even if our definition is more complex than theirs, that does not mean that they cannot comprehend the idea of being free.
It is stretching it to think that animals understand the intellectual concept of freedom, but they are capable of feeling that their natural, maybe I should say their instinctual, desire for freedom of movement is being constrained. It seems a contradiction to me to think that it is not realized by animals that they are lacking something in their lives that is essential to their well being.
They obviously do not understand the definition of freedom the way people do. Any animal that you put in a cage knows that is not how there life was meant to be lived. They say dolphins try to commit suicide when they get trapped for to long. While, that is supposedly just a theory and controversial. I can see that happening with how smart dolphins are. Animals are not meant to live in cages.
I don't think any animal can embrace freedom in the abstract way that we endorse in rhetoric. I think what we all want is actualization or the right environment in which to develop at a pace that is level to where we are at. For a predator like a wolf or leopard this might mean having the impression of wandering and hunting game. For a domestic animal like a cow this might just mean grazing in safety. For a human this means more. I think a human needs to be able to progress from one mode of understanding to the next unimpeded to have a true sense of freedom. Still, All of these are manageable if we are smart enough, And none are pure perfect freedom.
By the knowledge of body language everyone has a sense of zone. An animal would have a periphery of say 5 meters. If you encroach that space they might feel uncomfortable. If you make a cage that is say 2x2 meters (smaller that his private zone) the animal is bound to feel uncomfortable. But if the cage is bigger than this that's it. Even if they are caged they won't realize it. A lion would require a cage of 25 sq. Km. We humans are caged in to our own houses and countries but the boundaries are so massive that we don't realize it. But the minute we want to step out in to someone else's house (or country) we'll be stopped. So, let alone the freedom of animal we ourselves do not understand freedom in it's true sense. I don't think an animal would understand this.
Animals simply aren't intelligent enough to understand a concept like freedom or a concept of any other kind as a matter of fact. It is true that humans are animals, but people are of a higher order. No animal wants to be cage, but I think this is reflexive and instinctual. Perhaps some higher mammals can understand freedom in the most rudimentary sense.
Animals don't understand freedom, but they may understand more than humans by living entirely through the processes of their biological programming without the potential for self-harm, emotionally or physically, that comes in the form of self-consciousness and conscience. Animals are not capable of understanding freedom, but behaving the way they know they are trained to behave without question may indeed make them even more free than we could ever be.
I do not think that animals are capable of understanding freedom. Animals do not possess the ability to comprehend something like freedom. I think that only humans can truly understand what the meaning of the word freedom is all about. That doesn't mean we shouldn't continue to fight for animal rights though.