There is a practical reason for all those counselors and professors to urge you to get that summer job or intern experience when you are in college: It's called "getting a job." Once you leave your university grounds, the first question you are likely to hear during your job interviews is "What sort of experience do you have?" Although a degree provides you with knowledge of a subject, experience out in the work world gives you the ropes to know how that knowledge applies to work performance. At times it can be frustrating that the HR manager is more interested in your job over the summer selling ice cream than they are with 4 long years you spent at college, but how you perform in the workplace is the best criteria for how well you will do in your new job.
As a result, it's to your advantage to get as much relevant experience to the job you'd like to take on. Even a job as a "go-fer" in your relevant field will add clout to your resume. Unless you are in a highly technical field, most college graduates will start at the ground level and work their way up. A good college degree may open a door, but you've still got to demonstrate why your work skills make you suited to the opening you are applying for. Being able to say you worked in the field for which you are applying will give you the clout you need to land the job.
In addition, being able to call on those people you worked with to act as references is another important advantage you gain from having work experience in your field. Those summer bosses and intern managers are in touch with others in the business. Often they can give you names of people to talk to for advice when you are job hunting or tell you about professional organizations in the field who have job banks in your relevant industry. Having a good reference from someone in the music business when you are applying for a career in music is better than having your dad's best friend or the owner of the ice cream shop give you a good review.
If you don't have experience (even unpaid volunteer work) in your field, don't despair. Summer jobs and other work experience still gives you a history in broad areas such as taking on responsibilities, being on time, working hard, and other attributes any future employer will be interested in. However, it is the pertinent experience that will serve you best. Working in your industry of choice, whether as a volunteer or paid employee goes a long way toward demonstrating your interest and knowledge of the field.
The most important factor in building a great resume and presenting yourself to any future employer is to show what sort of a worker you are. Paid your own way through college? You'll impress the guy who created his business from scratch. Volunteered in your industry to gain skills? You'll show a potential employer you want the knowledge and are willing to work (even for nothing) to get it. Worked at an entry level job in the business? You've struck gold with future employers, and can build from there. You've got an advantage over the college-only applicant, every day of week.