Garbage harms animals because they can choke on it. For example:penguins: you know the plastic around the cans of soda? These can choke a lot of animals.
Garbage can be put into several categories that impact animals:
Food scraps in trash bins and dumps attract large numbers of animals to the free buffet. Insects attracted to the rotting food are a vector for disease. Vermin, like seagulls and rats, multiply and eventually spread out into the surrounding community. Others like bears lose their fear of humanity (become acclimatized to humans). When this happens they become a danger eventually leading to conflict which implies damage to someone and death to the bears.
Toxic waste kills animals by directly poisoning them, affecting their reproductive ability, and causing teratogenic impact (deforming their offspring). These impacts are from the garbage itself and from leachate reaching groundwater or surface water.
Waste sites and dumps can cover large areas of land impacting ecosystems. In water it acn cover access to breeding areas and cover the egg depositing areas.
As pointed ou in Answer #1 animals can become tangled with six pack plastic holders, broken bottles wire and fishing line which reduces their chances for survival.
Whenever there is an accumulation of garbage there is someone who wants to reduce the problem by burning it in situ. This practice can lead to uncontrolled brush fires with their associated eco-damage.