atomic orbital
Imagine trying to photograph a fly that buzzes around a lamp far too fast to follow. You cannot pin down where it is at any instant, but if you left the shutter open for a long time you would get a fuzzy cloud — thicker where the fly spends most of its time, thinner at the edges. An atomic orbital is that cloud for an electron around a nucleus: a map of where the electron is likely to be found, not a track it travels along.
More precisely, an atomic orbital is a mathematical function (a wavefunction) that comes out of solving the Schrödinger equation for one electron in an atom. Its square at any point tells you the probability of finding the electron there. Each orbital has a characteristic shape and size — spheres (s), dumbbells (p), cloverleaves (d), and more — set by three quantum numbers, and it can hold at most two electrons.
The honest caveat is that orbitals are not little planetary tracks, despite the old word 'orbit'. The electron does not follow an edge; the orbital is a region of probability. And strictly speaking, clean orbital shapes are exact only for one-electron atoms like hydrogen; for many-electron atoms they are excellent, widely used approximations rather than perfect truths.
The lowest orbital of hydrogen, called 1s, is a simple ball of probability centred on the nucleus: the electron is most likely close in and ever less likely the farther out you look, though it never quite drops to zero. A 2p orbital, by contrast, looks like two lobes on opposite sides of the nucleus with a clean gap in between.
An orbital is a probability cloud with a shape, not a planetary track.
Do not confuse an orbital with an orbit. An orbit is a definite path; an orbital is a region of probability that can hold up to two electrons of opposite spin.