Typically founders are product people, they want to solve a problem that exists in the world. But, to solve that problem, they need to make a big impactful company, that grows to dominate a particular niche or industry and disrupt the current way of doing things.
To these founders, "billion dollar company" is a shorthand for all these ideals: to make a great and lasting company, to solve a real problem for a very large number of people, and to make a real impact in the world.
It's not coincidence that this phrase is also important to VCs, for whom "billion dollar company" may have a different meaning, that being "make back the fund for our LPs". I say "may" because that's a simplistic view: many VCs are looking to make the world a better place too, and in many cases they have more money than they need already.
And to journalists, these mean "companies which we have to pay attention to". And when you think about, they're not paying attention because of the value, but because of the impact. Which is why journalists are always talking about consumer companies, because they have much more impact in the world than more successful enterprise companies.
Of course, that's not to say there aren't people in it for the money. But we rarely need to worry about them, since they rarely succeed.