It's about the surprisingly subtle logical structure underlying how we use noun phrases; about qualifiers like "a", "some" and "the"; about a perhaps-surprising feature of language, namely that to the best way to explain what some term means may involve explaining how to rewrite whole sentences including that term in a different form.

The explanation for why "The present king of France is bald" is the example Russel gives, where it might be hard to say this statement is false when there is no current king of France.

Another interesting example is "The average woman has 2.2 children." If you intuitively think that noun phrases refer to things (rather than sets), you'd have to admit the existence of some sort of an "average woman" and the property of having 2.2 kids.