The term "turn out" refers to the amount of rotation a dancer has in their legs, used mostly in classical ballet, from the hip socket right the way down to the ankles and feet. Unfortunately genetics play a big part in the amount of turn out each dancer is able to utilise, due to the alignment of the hips and the movement available in the hip joint. However, turn out can be worked on in order to improve it, just as a dancer would practice their pirouettes or work on their flexibility.
A large part of the act of "turning out" is the effective utilisation of the muscles surrounding the hip joint, such as the gluteus medius (on the outside of the hip), the adductors (running down the inside of the thigh to the knee) and the deep muscles of the gluteus maximus (a dancer's derrière). The muscles must be strong enough and ‘useful’ enough to be able to turn the hip out from the hip.
Many dancers are not aware that turn out comes from the hip, not the feet. This is to ensure that the knees are also turned out and are not at risk of damage from twisting and straining to support the body when it requires turn out. The adductors work to keep "wrapping" the leg muscles around each other from inside to out and the gluteus medius maintains the "turned out" shape of the upper legs and lower back by working hard to keep these in place. In the meantime, the deep gluteus maximus muscles are constantly fighting the natural human form of parallel legs and feet: it is not just the external muscles which are working hard.
Therefore to improve your turn out, ensure your muscles are strong and working correctly, and ask your teacher if you aren't sure.