The Outer Ring connects the four quarters of Naxxramas. Depending on which quarter you are in, you will encounter enemies ranging from spiders to death knights. Shades patrol the Outer Ring, constantly making a habit of appearing out of nowhere.
Though the Outer Ring connects each quarter, the ends are blocked off by a wall. This prevents raids from only having to clear one quarter to access other quarters 'end' bosses.
In the original version of Naxxramas, the Outer Ring contained enemies from every wing (ghouls, gargoyles, death knights, necromancers, plaguehounds, spiders, and more). They also contained Frozen Runes in the now "unused" area, which gave raids reason to progress further beyond the final boss rooms.