There are many connections between animals and their habitat, and some of these are crucial to an animal's survival. Some examples include the available food selection in particular places, physical adaptations to particular environments, and instincts for surviving in certain conditions. To some extent, many environments are also dependent on the presence of certain animals, because living creatures can have huge impacts on ecosystems, and everything can be disrupted if the balance changes.
One of the most well-understood connections between animals and their habitat is the question of food. Some animals are very dependent on particular food sources, and this totally ties them to a certain environment. For example, panda bears primarily eat bamboo, so bamboo forests are very important for their survival. Some animals are able to find alternate foods if they are transferred to another area, and some are less versatile.
Another common connection between animals and their habitat is physical adaptation. Some animals have adaptations that make it very easy for them to live in certain environments. For example, an animal might be colored in a way that allows it to camouflage in a particular environment. Another example would be animals that have adaptations which allow them to survive in particularly harsh conditions, such as long fur in arctic zones.
Sometimes behavior is the main connection between animals and their habitat. For example, many creatures have innate behaviors that drive them to target certain foods or avoid certain poisonous items. If those animals are placed in another part of the world, they might fail to find anything to eat, or poison themselves. Also, any advantages they have because of their behavior would probably fail to help them in the new environment, so they might simply be shoved out by other creatures with more fitting instincts.
Another thing that makes a big difference when it comes to animals and their habitat is the issue of balance. In its own natural habitat, an animal will generally fit into the overall scheme of things. There will normally be enough food for it to eat, and its presence won't generally throw the ecosystem into chaos. If the animal is required to live in another environment, it might disrupt the entire balance of life, possibly causing serious problems in the ecosystem, and might even cause extinctions. Another possibility is that the animal might not be able to find enough room for itself in the ecosystem and can, therefore, fail to survive.