I'm a non-native English speaker, and I've been working with an accent coach to improve my pronunciation. The IPA chart has been instrumental teaching tool, and after about two years it's finally starting to sink in.

It's really helpful to understand the theory behind the pronunciation, instead of just repeating words and attempt to make the same sounds as my coach. As in "this is what your tongue should be doing, but you're doing this other thing instead."

You can even use the chart (and maybe Wikipedia) to identify specific reasons as to why you're doing something wrong. For example, there's just one way to pronounce "S" in Finnish, whereas there are four ways to do that in English. It's just something that never crossed my mind before starting to work with a professional.