You need to use X11 port forwarding so that the
gedit program can use your computer's display.
http://e.molioner.dk/guides/puttyx11
If you are on Windows (I presume you are since you are using PUTTY), you will also have to start an X display host. I recommend
XMing.
http://www.straightrunning.com/XmingNotes/
explanation
If you SSh into the other computer, and type
echo $DISPLAY
at the command prompt, you will be informed that the variable either doesn't exist or has a value of zero (or some other invalid value). This is because the other computer sees you as a TTY (a text terminal) as opposed to a GUI system.
All X GUI programs require this variable to have a valid value, so that they can 'talk' to the GUI display.
Once you do that, you should be able to use graphical programs over the X connection.
Keep in mind that the system you are dialing into may have the ports required to do that kind of thing closed. If that is the case, you will have to use a TTY editor. Try one of
emacs,
vi, or
pico.
Hope this helps.
[edit] Yeah...
reflectionX is good too... :-)