I've got an installation of Jenkins on a Ubuntu 14.04.5 LTS which I needed to update. In order to do so I did the following:
Download the new version (2.107 at the moment of writing this post). In
Backup the old version (Jenkins war is installed in /usr/share/jenkins):
sudo cp /usr/share/jenkins/jenkins.war /home/user/backup/jenkins-2.8.war
Overwrite the old jenkins.war:
sudo cp /home/user/backup/jenkins.war /usr/share/jenkins/jenkins.war
sudo service jenkins restart
Now, you're all set and you can start updating the plugins.