The explanation is fairly easy to find if you google Telefonvisitenkarte, however, I don't know of an equivalent term in English, I am just guessing here.

A top image over the telephone
Music on the telephone raises the awareness of your products and service. Made especially for your company, this contributes to your Corporate Identity. A company establishes a "phonetic presence" or an "acoustic business card" - and this for every branch.
http://www.speech-design.com/en/products/mozart/mozart-cd/de...



Market your product:
• Marketing
Show yourself so I can buy from you
• Self-promotion
The exclusive brand 'I'
• **Acoustic business card**
Be pro-active and talk about it
• PR
Public Relations that work with your personality
http://www.entrepreneurhub.net/index.php?id=7


The voice on the phone is the **acoustic business card** of every single personality. Communication on the phone shapes the
competence and the image of your personality. To be convincing in individual and target-oriented telephone conversations
and to treat the conversational partner ideally, is the result of this phone training of "emotional intelligence".
http://www.ipecc.de/english/trainings.htm



You can compile your individual “acoustic business card” for your mobile with one click of a mouse creating a professionally recorded announcement at our www.callstudio.de/en website...Individual sound production is completed and archived in our own sound studio. Your “acoustic business card” will automatically be activated and within 2-3 days you will receive an SMS-reminder.
http://www.hiprocall.com/index3.php?page=handyansagen

I would say that the expression refers to the introductory presentation of the caller, which playsthe role of a business card when you visit your prospective customer in person. "My name is XXX; I work with YYY; our company is located [...] and [does such and such]"; thereafter, the caller will communicate further details, and try to sell her/his product, if the person on the other end does not hang up.