Back in the beginning of Burning Crusade, when heroic instances were originally introduced, you had to get to Revered standing with a dungeon's associated faction to buy a key that would let you into heroic mode. Later, that requirement was relaxed to Honored. This was taken one step further in Wrath of the Lich King, where there is, technically, no requirement to enter a heroic besides being level 80.

However, this doesn't mean you're ready for heroics (and Naxxramas-10, which is about the same difficulty) the moment you ding 80 and go train. This is something I found out on my own first 80, when I scratched and clawed my way through healing a heroic Old Kingdom in mid-70s dungeon and quest gear (we never did get the last boss down). I was told that I was rather undergeared for heroics, and to go do some normal-mode level 80 dungeons first (Halls of Lightning, Utgarde Pinnacle, Oculus, Culling of Stratholme).

This was some of the best advice I ever got in WoW. I ran each of the L80 normal-mode dungeons once, and my gear level improved by about 50% in the space of a day or two. There are some extremely serviceable quest rewards in all of these dungeons, not to mention drops and rep gains. There is also some excellent crafted gear out there, if you have some any spare change or mats kicking around. And from that moment on I wasn't that guy trying to tank heroics with 20,000 HP, or the DPS doing 1,000 in Naxxramas. Please, don't be that guy: run some normal-mode level 80s, and maybe pick up a bit of crafted gear or rep rewards, before you try to do heroics or raids.