Leadership is not necessarily something that is part of a class. No class is marked is a leader by their mechanics alone, in theory. That said, tanks often end up in leadership positions. This isn't always universal, of course, especially in well-organized raid guilds, where you may just soon see a healer or even a DPS player in charge. But if you've ever run Raid Finder, you know that it seems like 9 times out of 10, it's the tanks that set the pace and contribute quite a bit to whether or not the run succeeds.
Part of why this is just boils down to what's essential. A tank is generally the one who needs to pull, and a tank needs to be present and working for a pull in 5-man or raid content to succeed. If a DPS or healer pulls, you'll probably get wiped. Sure, it's possible to survive a pull without a tank if you're lucky and your DPS and healers have some skills, but eventually, especially as you get to boss fights and high end raids, you will need an attentive and competent tank to survive the vast majority of pulls. So in a way, it could be a mechanics thing that ends up slapping tanks with the leader role after all. It's not that they want, deserve, or are otherwise drawn to it, it's just that in your average pickup group where almost no-one knows each other, the tank is in the best position to take control of the group and get things headed in the right direction.
The fine art of monster wrangling
As the tank, you will have control of the mobs that you're fighting, in theory. But keeping aggro on mobs is often only the beginning of the story. First, you have to wrangle them in, and second, you have to make sure they're properly positioned.
Blood death knights are in a good position in that we have some of the best tube to wrangle mobs and keep them them wrangled. Of course, the most obvious tool is Death Grip. When you can pull a mob away and keep them on yourself for an extra couple seconds, you have a lot of leeway to chase a runner. Another good wrangler is Strangulate. By silencing a caster mob for a few seconds, you force them to run to you, making it easier for you to keep aggro and for your DPS to catch them in AoE damage where appropriate. On the talent side of things both Chilblains (if you can justify giving up Death's Advance, which is also immeasurably useful for chasing down mobs and positioning them quickly) and Gorefiend's Grasp offer opportunities to keep mobs snared or pull them back to you. If you can spare the glyph slot, you can even glyph Death and Decay to provide a snare.
Once you have the mobs wrangled and glued to you, positioning is the other thing to get right. Some mobs have a frontal cleave or a cone magic or breath attack. It is your responsibility as a tank to make sure that attack doesn't hit your healers or DPS. Now, your DPS and healers should know to stay away from the front of the mob, but that can be hard to do if the tank doesn't have the mobs under control and steady.
Positioning is also important in how it relates to where you position the mobs. If you're in an area where there's trash patrols, or another group of mobs standing a few feet away, you need to make sure you don't actually pull another group. Pulling the mobs back a little bit can be the difference between success and a wipe. In addition, you need to make sure the mob is positioned to allow your DPS and healers to stay in good positions themselves. If you're fighting near a ledge, for example, or if a boss drops a void zone, and you tank the boss with its back to the ledge or void zone, you may have just left your melee DPS high and dry. If they can't get the back of the boss, they may be forced to DPS at the sides, or worse, at the front, where they'll be susceptible to cleaves and lose damage from being parried.
Know your fight
This ties in a bit to leadership in the long run, but it's worth mentioning as its own separate issue. Really, in a perfect world, everyone would know the fights. If they hadn't directly experienced them, they would have read previews and guides to give them a good idea of what's going to happen and what they need to do.
In reality, there's a good chance, especially in relatively new content, that someone is going to walk into the instance without having a clue of what's going on. In these cases, it generally defaults to the tank to know what's going on and keep them up to date. From time to time, you will get a DPS or healer chiming in (or if you're really unlucky, you'll get multiple people chiming in with differing opinions on how the fight works), but for the most part, people expect the tank to know what's going on.
This may seem a bit unfair, but knowing the fight does at least offer you a chance to figure out positioning ahead of time, and you can make your life easier by making sure your group mates know when they have to deal with adds, or when they should stack in a certain place, or so on.
So in that case, knowing the fight can end up making your life easier, and while you can certainly choose to stand on principle and let everyone else learn the fight themselves, sometimes being able to explain stuff means you get your valor points quicker, and some days, that's all you really want.
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.