The TERM environment variable is used by your terminal emulator to indicate which type of control string it supports. For the most part you should not override this variable, but there is a narrow set of circumstances where the default value can be incorrect or at least not optimal.
For example in most distributions the default value for a console terminal is linux and for a graphical terminal xterm. That’s fine, but don’t allow you to enjoy vim or screen 256 color mode in graphical mode.
A traditional xterm only supports 16 colors and this value is specify into the terminfo database.
As you can image, changing the xterm entry would have made users of the newer versions happy but also broken the configuration for others. Instead a new value xterm-256color was declared. That may seems fine but when you log in remotely to machines with an older terminal database, the value isn’t recognized.
In this case the only viable solution left is to override the TERM value in order to unset the 256 color mode. You can do it by adding something like that to the .bash_profile on the remote machine:
if echo $TERM | grep -q -- '-256color'; then
export TERM=`echo -n $TERM | sed 's/-256color//'`
fi