Outside of weightlifting, stiff-legged deadlift usually refers to a similar looking motion that instead begins each rep with the bar resting on the floor (an actual deadlift in stricter terms). In weightlifting, it’s usually synonymous with the Romanian deadlift or RDL, as described here. Just be sure you know what whoever prescribed them to you is actually looking for.
Stand in your snatch or clean pulling stance with a clean grip on the bar. Set your back in the same extension you use to pull the snatch and clean and brace your trunk forcefully. Actively keep the bar as close to the legs as possible throughout the motion.
Hinge at the hip while bending the knees very slightly to bring the bar as far down the legs as possible without losing any back extension.
Stay balanced evenly over the whole foot rather than pushing the hips back more than necessary and shifting to the heels. This will limit how much weight you can handle, but it will make the exercise more effective by increasing the force on the hips and back while reinforcing the balance we want in the snatch and clean.
Stay braced tightly so as you change directions at the bottom, you don’t allow any softening of the back extension.
If you’re mobile enough to get the plates to the floor with perfect back extension, still stop just short of touching—the changing of direction without compromising back extension is an important element of the exercise.
Historically I’ve differentiated between the RDL and the stiff-legged deadlift, but over time I’ve come to decide the minor difference isn’t worth the headaches it creates. In the RDL, the knees would remain in the very slightly bent position all the way through, and in the stiff-legged deadlift, each rep would start and end with straight knees in the standing position. This makes the RDL emphasize the glutes slightly more than the stiff-legged deadlift, and somewhat mimic the scoop of the snatch and clean. However, the differences are extremely minor—do whichever variation you find more effective.
The stiff-legged deadlift strengthens isometric back extension along with the glutes and hamstrings. It also strengthens the lats and shoulders because of the effort to keep the bar close to the legs with the shoulders in front of the bar. It’s used to support stronger pulling for the snatch and clean.
Sets of 3-8 reps are most common. Weights usually start around 40% of the lifter’s best back squat and often be very heavy, sometimes as much as 70% of the back squat.
The stiff-legged deadlift can be done with a snatch grip, or without lifting straps (or hook grip) for more grip strength work.
Too much knee bend for you at the bottom. By the time the bar is at your knees you are fine, but you want to keep them stiff and maintain that back arch past the knees.