Why does philosophy of language matter? I'm not trying to troll here; I'm interested in what people who find this subject fascinating are so fascinated about!
This probably has to do with the so-called "linguistic turn": during the 20th century it has been considered (Wittgenstein, logical empiricists, ...) that the role of philosophy is not answering big questions, but only clarifying what we mean, analysing our language, in contrast with science whose role is to test our claims empirically. That was the beginning of analytic philosophy. Following this view, philosophy of language certainly plays a central role. Note that Quine famously denied that factual (synthetic) and linguistic (analytic) components can be so well distinguished, but he did so by appealing to arguments in the philosophy of language.
Another related way to express the importance of philosophy of language is that arguably, language is at the foudation of any kind of knowledge or representation of the world. For example the content of a scientific theory is expressed by mean of language. It follows that many deep philosophical questions (whether our scientific theory describe reality or are mere predictive instruments, whether they reduce to claims about the observable or not, whether there are natural kinds in the world) can be reframed in the philosophy of language: how language relates to the world, or what is the meaning of meaning. For example, the reduction of one scientific theory to another can be expressed as the mapping between different vocabularies.
Another (still related) issue can be found in the work of Frege, or Tarski and others, which bridges logic, mathematics and semantic.