What it strengthens:
Gluteus medius and minimus, obliques (a little)
The gluteus medius and minimus aren't as well known as the gluteus maximus but they are very important for pelvic (hip area) stabilization, are mainly responsible for your ability to balance on one leg (as you do when you walk, go up stairs, etc), and help keep your butt perky!
Standing tall (and optionally holding on to a chair/counter for balance), stabilize your body by keeping your stomach pulled in and your standing leg strong and in place. Lift your other leg straight out to the side (using your butt) as high as you can without pain and while keeping your toes pointed forward. Hold a moment at the top and return to start. Complete all repetitions on one side and then repeat on the other leg. When you feel a burn in your hip socket, you know it's working! Make sure you aren't just leaning over to the side to make your leg go higher.
To make easier:
Don't lift your leg as high and/or don't hold it at the top.
To make harder:
Do not hold onto anything for balance, but use your core instead and/or hold for longer at the top of the movement and/or lift and lower more slowly.