LMDE (Linux Mint Debian Edition) is a very exciting distribution, targeted at experienced users, which provides the same environment as Linux Mint but uses Debian as its package base, instead of Ubuntu.
LMDE is less mainstream than Linux Mint, it has a much smaller user base, it is not compatible with PPAs, and it lacks a few features. That makes it a bit harder to use and harder to find help for, so it is not recommended for novice users.
LMDE is however slightly faster than Linux Mint and it runs newer packages. Life on the LMDE side can be exciting. There are no point releases in LMDE 3, except for bug fixes and security fixes base packages stay the same, but Mint and desktop components are updated continuously. When ready, newly developed features get directly into LMDE 3, whereas they are staged for inclusion on the next upcoming Linux Mint 17.x point release. Consequently, Linux Mint users only run new features when a new point release comes out and they opt-in to upgrade to it. LMDE 3 users don’t have that choice, but they also don’t have to wait for new packages to mature and they usually get to run them first. It’s more risky, but more exciting.