Explanation
At the core, this formula is extracting characters starting from the left, and using the FIND function to figure out how many characters to extract.
First, FIND looks for the "@" character inside the email address "achang@maaker.com". The "@" character is the 7th character so FIND returns 7. The number 1 is then subtracted from 7 to yield 6. This is done to prevent the formula from extracting the "@" along with the name. The LEFT function then extracts 6 characters from the email address, starting from the left. So:
=LEFT(C4,FIND("@",C4)-1)
=LEFT("achang@maaker.com",FIND("@","achang@maaker.com")-1)
=LEFT("achang@maaker.com",7-1)
=LEFT("achang@maaker.com",6)
="achang"