LMDE repo are at the moment snapshots of Debian Testing. Currently, our repo looks like Debian testing repo in January.
Additionally with that LMDE provide a repo for Linux Mint specific packages: Cinnamon, Nemo, Mint Sources, Mint Update...
To update your system, you can use either apt or Mint Update. The second one is recommended for new comers as it allows you to read carefully the know problem before upgrading. LMDE and Debian are 100% compatible. You can read the Debian Handbook if you want to learn more about Debian or you can start with this: viewtopic.php?f=197&t=159257
If I have seen further it is by standing on the shoulders of giants. [Isaac Newton]