It is characterized quite catchy by its developer:
I want to organize my computer and my activities myself, I do not want my activities to be tracked or stored at a hidden place, if I was not asked to allow that. Who knows who can misuse this data in the future? I don't see any use of this service for myself. Therefore I deinstalled it. But I am concerned, that it might be reinstalled with the next Update Pack.zeitgeist is a service which logs the users's activities and events (files opened, websites visites, conversations held with other people, etc.) and makes relevant information available to other applications.
https://launchpad.net/zeitgeist
I am suggesting that zeitgeist should be removed from the default installation of LMDE Mate. If there are no strong arguments - for instance functionality of the Gnome-3 based CInammon, integrity of the Ubuntu kernel -, then it should be removed from all Mint editions. People, who want to use it, are still able to install it via synaptic or the software centre. Another possibility would be, that the installer is giving the user a choice during the installation: the default setting should be "No".