CTFs generally have four to 6 catetories on a range of topics. Four of these categories are Web Exploitation, Forensics, Reconnaissance, and Cryptography.
This category involves finding and exploiting vulnerabilities in websites. For a more detail description of this type of attack, look at SANReN Cyber Security Challenge's page on Web Exploitation.
This category involves recovering information from files and data. For a more detail description of this type of challenge, look at CTF 101's page on Forensics.
This category involves gathering information about the targeted network or system. For a more detail description of this type of attack, look at Medium's Article on Network Reconnaissance.
This category involves translating data into an encrypted form for security. For a more detail description, look at IBM's page on Cryptography.