What impact does reading have on improving one's writing abilities, and what should writers focus on?

To me, reading enhances writing skills by expanding vocabulary and exposing writers to a variety of styles they might admire. It also serves as a personal challenge, pushing me to grow and refine my craft.

As an admissions editor, I help applicants who are writing essays to get into their dream schools. Unfortunately, we don't learn how to write personal statements in school. Applicants from cultures where humility is important often struggle to highlight their strengths. Reading excellent samples of application essays is a great way to get started. As you read a sample, jot down words and phrases that appeal to you, and think about why you like them. Then, consider how you could incorporate some of these words and phrases into your own story! 

I think I've said this twice now, but reading is so important. If you're not reading, you're not improving your writing. The wonderful thing for nonfiction writers (especially those who need to cite their sources) is that they (we) get to read on a daily basis. 

For fiction writers, there has to be a concerted effort to read fiction - and to read fiction in the genres that you (we) specialize in. 

Reading and writing go hand in hand - no question about it.