Short answers, pulled from the story.
An atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. It describes the electron's charge distribution around the nucleus and is used to calculate the probability of finding an electron in a specific region. Each orbital is characterized by three quantum numbers: n, ℓ, and mℓ.
The names s, p, d, and f come from early spectroscopists who described series of alkali metal spectral lines as sharp, principal, diffuse, and fundamental. After f, orbital names continue alphabetically as g, h, i, and k, omitting j because some languages do not distinguish the letters i and j.
Robert S. Mulliken introduced the term orbital in 1932 as shorthand for a one-electron orbital wave function. Niels Bohr had earlier, around 1913, explained that electrons might revolve around a compact nucleus with definite angular momentum.
An atomic orbital can be occupied by a maximum of two electrons, each with its own projection of spin, one spin up and one spin down. The Pauli exclusion principle states that no two electrons in an atom can have the same values of all four quantum numbers.
The repeating blocks of 2, 6, 10, and 14 elements in the periodic table arise from the number of electrons that fill a complete set of s, p, d, and f orbitals. Niels Bohr first proposed in 1923 that periodicity in the elements comes from the periodic filling of electron energy levels.
In non-relativistic quantum mechanics, an atom with atomic number greater than 137 would require its 1s electrons to travel faster than the speed of light. Richard Feynman first pointed out the significance of element 137, informally called feynmanium with the symbol Fy, though the true critical value where the vacuum breaks down occurs near Z of about 173.