To find links you need to use regexps. For example this Stackoverflow question answers how to find urls in text: Regex to find urls in string in Python
It looks like this in Robot Framework:
*** Settings ***
Library re
*** Variables ***
${mailbody} this is mail body http://www.stackoverflow.com/ foobar https://stackoverflow.com/questions/31288261/how-to-click-the-link-in-email-body-and-how-to-spot-out-the-link-using-robot-fra
*** Settings ***
Library re
*** Variables ***
${mailbody} this is mail body http://www.stackoverflow.com/ foobar https://stackoverflow.com/questions/31288261/how-to-click-the-link-in-email-body-and-how-to-spot-out-the-link-using-robot-fra
${url regexp} http[s]?://(?:[a-zA-Z]|[0-9]|[$-_@.&+]|[!*\(\),]|(?:%[0-9a-fA-F][0-9a-fA-F]))+
*** Test Cases ***
Get Urls
@{lines}= re.findall ${url regexp} ${mailbody}
Log Many @{lines}
You cannot really click the links, instead you should use Selenium2Library to open them in browser.