The deadlift is called the "dead" lift, not because it kills you, but because the weight is dead on the ground when you start. In most lifts you take the weight, lower it, and then lift it up. Deadlifting is different.
In the deadlift, the weight is on the ground as a "dead" weight and you pick it up with no preceding "eccentric" portion of the lift. Grossly speaking, there's two kinds of deadlifts: frame/trap bar deadlifts, and barbell deadlifts.
Barbell deadlifts are a lot more common, so I'll quickly get frame deadlifts out of the way. Here is Kalle Beck from http://startingstrongman.com demonstrating a frame deadlift. It's pretty straightforward: you stand in a frame loaded with weights, grab the handles, and lift it.
The "trap bar" is basically a small frame, hence I throw them together, though there are differences in deadlifting with a frame vs. a trap bar. I won't get into them here.
Barbell deadlifting is by far the most common form of deadlifting and generally takes two forms.
(I'm going to skip the Jefferson deadlift because only serial killers do Jefferson deadlifts.)
Conventional deadlifts are where you stand behind the bar, feet at a more or less normal width, and grab the bar with your hands outside your feet and legs. A good example of a conventional deadlifter is Konstantin Konstantinovs.
A "sumo deadlift" is where you put your feet outside your hands. A good example of a sumo deadlifter is Chris Duffin.
Generally speaking, the conventional deadlift uses more back strength and the sumo deadlift more leg strength. That's a sliding continuum though.
Some sumo deadlifters (like Chris Duffin) have a pretty narrow sumo stance, while others have a pretty wide stance, like Amanda Lawrence.
A sumo deadlifter with a narrow stance is using relatively more back strength than a wide-stanced sumo deadlifter, who is using relatively more leg strength.
In addition, some conventional deadlifters have a pretty narrow stance (like KK above), while others have their feet wide enough apart to almost be a sumo deadlift, but they still keep their hands outside their legs, like Jerry Pritchett.
In general, men under 200 lbs in powerlifting tend to prefer sumo to conventional by a 2:1 ratio, and it flips around once they go above 200 lbs, with the men preferring conventional by a 2:1 ratio.
Female powerlifters IIRC prefer a sumo stance across the board, but you still have some amazing conventional deadlifting women like Jessica Buettner, who is also cute as a freaking button.
There is a common misconception that a sumo deadlift is "cheating" because the range of motion is shorter since the legs are spread further apart. This is false. Some people are stronger in a sumo deadlift because of LEVERAGES.
The inverse is also true. Some people are stronger in a conventional deadlift than they are sumo. You should find which stance works for you, or you can simply do trap-bar deadlifts and avoid the issue entirely.
Deadlifting is often called the king of the exercises because it's a full-body exercise--hits some quads, some hams, a lot of glutes and back, etc. It works you from your feet to your head.
I think everyone should deadlift because the lower back is a very vulnerable point of injury for a lot of people as they get older. Good deadlifting is healthy for your back and strengthens it which can help prevent injury.
One last tangential point about deadlifting--it is well known that you should lift with a "neutral spine" to minimize the risk of injury. This doesn't mean that if your spine deviates one degree from straight that you're going to hurt yourself.
"Neutral" is a range of position, not exclusively truly straight. You can have a small amount of flexion in either direction without injury risk. That being said, it is always good to err on the side of caution.
Dr Stefi Cohen had a great post about this on her instagram page, but I'm not able to find it right now. If I stumble across it later, I'll try to tack it on the end here.
Fin.