Absolute - contains the full name from the root to the file. It is very clear what you are refering to.
Example:
/var/log/auth.log
Relative - it is related to current directory and contains the rest needed to get a file or directory.
Example:
If you are in /var the path log/auth.log is a relative path.
In relative path .. can be used to get to a directory up: ../log/auth.log is a relative path - if you are in /var/cache directory