~ is called a tilde
/ is call a forward slash
When you only see a ~ after your prompt it usually means you are in your /home/<username> directory
When you see a ~/<directoryname> means you are in a sub-folder in your /home/<username> directory (ie: Hanzerik@Hanzerik:~/public_html$)
Another way you may see it is $HOME ie(cd $HOME/folderfoo) would move you into the folder called folderfoo located in your /home directory
Code:
hanzerik@Hanzerik-Server:~$ cd $HOME <<--- Changes directories to /home/hanzerik
hanzerik@Hanzerik-Server:~$ cd /home/hanzerik/ <<--- Does the same thing as above but more to type if you don't use auto-completion (tab key)
hanzerik@Hanzerik-Server:~$ cd public_html/
hanzerik@Hanzerik-Server:~/public_html$ <<--- Notice the / after the ~ sign
ETA: The / right after your prompt, without the ~, means you are in the / (root location of your file structure).