What are orbitals?
Since the 1930s we define an orbital as a 3-D region where the probability of finding an electron is maximum. I personally don't follow such a definition, but it's fine as long as you are in school.
The electrons in an orbital are never stationary but are in constant motion, so that's the reason why we define the probability density, which helps one to locate the position and time (not simultaneously) of the electron in the orbital.
The shapes of the orbitals are the solutions of the Schrödinger wave equation.
Precise definition of an orbital is a 1e wave function.
We solve the equation and plot a graph of probability of finding the electron vs the distance from the nucleus.