Well, there's actually a lot of different kinds of plastics! It's a very broad term. Some break down a lot easier than others. However, most plastics get into you by eating things prone to eating tiny plastic pieces known as microplastics, like fish. What happens with most animals (humans included) is when the body doesn't know what to do with it and can't digest it, it stores it in a safely isolated part. They can still hurt you there, hermit crabs get notably docile to the point of not even wanting to fight over mates, for example, most organisms just don't (yet) know how to safely be rid of them. And then we eat them, not even knowing they're there, and the process multiplies.
As far as the leaching thing, and the other way you get plastic in you, is that a lot of cheap plastic breaks down when exposed to heat. This leaches poison into the food in the form of fumes, or actually very tiny pieces of the container being brittle enough to break off into the food.




