Being saturated with something has a similar meaning to being full of it. If a thing (X) is saturated with a liquid (Y), then X has lots of Y in it. Usually, when we use the word "saturated", it's in that sort of context. But you could use the word saturated in other ways. For example, there is the difference between saturated and unsaturated fats, which is to do with the molecules being full of hydrogen, or something like that. Also we can use the word "saturated" metaphorically - so a poem could be saturated with meaning, perhaps - i.e. full of meaning.

To add to previous comments, I have also often heard of various job markets as being saturated. For example the job market for online English teachers is saturated (as in, it is full at at capacity). We could also use 'over-saturated' when something is too full.

One example occurs in photography. A saturated color is one that is intense. A red traffic light is a highly saturated red, but a pinkish color like a rose wine is not a highly saturated color. White and gray are completely unsaturated because they have no color at all.