The first sentence of the article says it all. Calligraphy IS letters, but letters shaped or formed in a very artistic way so as to convey beauty themselves.
For a quick example, if you type a wedding invitation in Times Roman font, it conveys the information required, but in an official, cold, unaffecting way. If the wedding invitation is written in calligraphy, the curvy letters convey a regal beauty befitting a wedding announcement.
To put it crassly, calligraphy amounts to pretty letters.