The cuticle around your nail may look rough and raggedy, or somewhat stretched and unattractive, but its main function isn't to look good. It's there to keep your nails safe from harm. Think of it as a protective eyelid for each nail. Cutting it away leaves your nails more vulnerable to fungal and bacterial infection. In a salon, where there may be an increased risk of infection anyway, don't make matters worse. Leave your cuticles intact, and if the nail technician recommends removing them, politely decline.
Instead, soak your nails for 10 to 15 minutes in warm, soapy water and then push the cuticles back gently with a towel before you visit the salon. You can also use a cuticle remover that sloughs off the dead skin but leaves the living tissue intact.