What a hydrogen orbital represents
An atomic orbital is not a path the electron travels but a probability distribution: the regions of space where the single electron of a hydrogen atom is most likely to be found, obtained by solving the Schrodinger equation for the atom. Each orbital is labeled by quantum numbers: the principal number n sets energy and size, the angular momentum number l sets shape, and the magnetic number m sets orientation.
The square of the wavefunction gives the probability density, often drawn as a cloud or as a boundary surface enclosing most of that probability.
Shapes of the s, p, and d orbitals
An s orbital (l equals 0) is spherically symmetric; the 1s is a simple sphere and higher s orbitals add concentric nodes. A p orbital (l equals 1) is dumbbell-shaped with two lobes and a node at the nucleus, coming in three orientations along the x, y, and z axes. A d orbital (l equals 2) is more complex, typically four-lobed, with five orientations.
Higher orbitals also gain radial nodes, surfaces of zero probability between regions of density. Hydrogen is the textbook case because its single electron lets the equation be solved exactly, making its orbitals the reference shapes used to describe all atoms.