This is a set phrase that we use in business communication. Write this when you're contacting someone who you don't know well and hoping that they will respond.
For example, you can write this if:
- You're a salesperson sending an email to someone that you hope will become a customer.
- You're writing a cover letter to apply for a job.
- You're trying to get a magazine to write a story about your business so you're writing to one of the magazine's editors.
"I look forward to hearing from you" sounds polite but also confident.