The phrase "writing in business" might seem rather daunting. But essentially any piece of writing that's connected to your career as a professional counts as "business writing."
Effectively translating your skills, desires, and personality through words (especially in the succinct manner required by most kinds of business writing!) is difficult, and takes *practice, practice, practice.*
Since a lot of us aren't "business" majors, let's focus our attention on three types of business writing that we'll probably all have to do at some point: résumés, cover letters, and personal statements.
A good résumé communicates only the most crucial components of your work. It's succinct, clear, and not overly wordy. Résumés aren't the place for elaboration. Cover letters and personal statements are documents more suitable to carefully-constructed elaboration. A strong résumé is also a targeted document. For example: if you're applying to an MA program in Chemistry you should probably cut high school experience from your résumé. Here's two resources on the basics of strong résumé-writing, one from OWL Purdue and one from UNC's University Career Services.
What concepts and ideas are integral to your portrayal of yourself in a business context?
Cover letters: basically an elaboration of your résumé? THINK AGAIN! Cover letters and résumés should of course work in sync, but a strong cover letter doesn't simply elaborate on what you say in your résumé: it instead provides a moment for you to convince your potential employers that you will indeed contribute positively to their company/organization. What values, experience, and skills do you have that will help make the company/organization you're applying to an even better entity? Here's two more resources on cover letter basics: https://owl.english.purdue.edu/owl/resource/723/03/ and https://careers.unc.edu/students/resumes-and-letters/cover-letters.
What elements of your self do you want to shine forth in the documents you send out to apply for jobs?
Personal statements: they're a lot like cover letters in the sense that you shouldn't simply elaborate on your résumé, but rather you should focus your attention on conveying how your qualities, skills, and experience would be an ideal fit for the company/organization to which you are applying. Since the OWL Purdue is such a useful resource, here's another resource from them on personal statement writing: https://owl.english.purdue.edu/owl/resource/642/01/. The Univ. of Illinois also has a helpful resource available for personal statement writing: http://www.cws.illinois.edu/workshop/writers/tips/personalstatement/.
To ask a metaphorical question, what threads will you choose to hold you together as a promising candidate?
Excellent business documents are the result of careful planning, research, and REVISION.