The exercise performed by lying on your back and raising your legs perpendicular to the floor is a leg raise.
In the lying version, the exerciser starts supine on the floor and lifts the legs mainly at the hip. The iliopsoas, a group of hip-flexor muscles, is a major target, while the abdominal muscles work to stabilize the pelvis and spine. Keeping the lower back gently in contact with the floor is commonly emphasized for controlled form.
“Leg raise” is a broad term covering lying, seated, hanging and side-lying variations. A hanging leg raise is harder because the torso is suspended and the pelvis can move more freely. A knee raise is related but usually bends the knees, reducing the lever length and changing the difficulty.
The movement is often described as an abdominal exercise, but it is not the same as a sit-up or crunch: those primarily involve curling the torso, whereas a leg raise chiefly moves the legs through the hip joint.