From their website:
cURL is the name of the project. The name is a play on ‘Client for
URLs’, originally with URL spelled in uppercase to make it obvious it
deals with URLs. The fact it can also be pronounced ‘see URL’ also
helped, it works as an abbreviation for “Client URL Request Library”
or why not the recursive version: “Curl URL Request Library”.
http://curl.haxx.se/docs/faq.html#What_is_cURL