I think Telephone API is a way to integrate software into telephone systems using an Application Programming Interface. Check below link to the book related to Telephone API , hope it will help you.
http://books.google.co.in/books?id=OBck_Mkji88C&pg=PA51&lpg=PA51&dq=telephone+API&source=web&ots=0FawUMX8bL&sig=f2kWR9b_cvLDwY6zUGidtygYTb8&hl=en&sa=X&oi=book_result&resnum=7&ct=result#PPT1,M1