Why is an interview important to hire an employee?

Interview will be the main tool to collect the necessary facts, both structured and semi-structured from which employer can collect the clear view of the employee.
It will be easier to find how the employee looks like and how he/she is confident in his/her presentation so an interview plays a vital role to select an employee.

The interview is the major method for hiring any candidate as it the candidates' opportunity to present himself to the employer and reflect his competencies relevance to the job post.
Although now there are other new complementary methods for the interview yet still the face-to-face interview is the primary method as it enable employers to have better judgment on the candidates' psychological behavior.

to let you know how you will hire very well.

Why is love important in a relationship? :).

To get an idea of the employee and the extent of his skills

any employment is a courtship (may be marriage if you continue long) between an employer and an employee, so proper understanding amongst each other before the final rituals, rites get performed (getting appointed) is necessary and thus background check, ability check, competency check etc are made aware to each other.
So interview is a platform to help both to decide to start the relationship or not

New answer to: Why is an interview important to hire an employee? Interview is very important in the hiring process of an employee in any organisation because, the interviewers try to ask questions that, in their experience, will give them the information needed to make the selection of the best candidate for the job.
Generally, a résumé is a reflection of the applicant in the eyes of the reader, This is because first impressions are lasting ones and a résumé is often the vehicle to either make a good impression or a bad one." at interview you'll be responsible for making sure a“ Square peg is put in the Square hole” and not “Square peg in the round hole”.
Interview is very important because it’s a two way learning process, it provides opportunities to both the employer and the employee as the employer will gain new knowledge on how to move the company forward and employee learn more about the company in the course of preparing for an interview.

The importance of interview before hiring can easily be understand by simply what people do in marketing.
You present or market yourself in some company before the interviewer and convince him/her that you the most suitable candidate to be hired.
You sell your services.
The better you are in position to market yourself the higher the chances to get an offer.
So, the hiring manager is a customer and you are the product convincing the manager that you are the best among others.
And by interviewing manager knows how much of benefit a candidate would be for his company while assessing him from the way he/she would enter in room til leaves the room.
Kay

as a simple answer i can say : it gives u as an employer direct feedback and measurement about the candidate when other tools may not be efficient .

"Are you willing to buy something you don't know what it is for?"

It’s also the only why for employee to shine in a group of candidates, The most important thing you must do in every interview is to ask great questions.
Here are9 great questions you can use or make your own on your next job interview:1) Who would make the ideal candidate for this position?2) How will the work I’ll be doing contribute to the organization’s mission?3) What were the best things about the last person who held this position?4) What are three ways I can contribute to the company beyond the job description?5) How can I best contribute to the department’s goals?6) How do you see me best contributing to the corporate culture and morale?7) What do you see as the biggest challenges of working here and how can I overcome those challenges?8) What is your vision for where the company or department will be in one year? In3-5 years?9) How can I best help you and the team succeed?