A Rydberg atom has one or more electron(s) which have energy levels almost sufficient for the electron(s) to escape the atom. Such atoms are called “excited.” They respond in an exaggerated manner to electrical and magnetic fields. The high energy level of the atom is due to having one or more electrons distant from the nucleus and loosely bound to it.
Rydberg atoms are large in a special sense. The distant electron(s) form an enormous cloud (orbital) around the nucleus. For example, in a famous experiment* with a Rydberg rubidium atom, an electron in the 51st shell from the nucleus was exposed to electromagnetic radiation. The radius of this cloud was 125 nanometers (125 billionths of a meter). This is 2,500 times larger than an ordinary atom.
Rubidium is not a small atom to begin with; it has 85 protons and neutrons and 37 electrons. But the Rydberg state of the atom is not dependent on how many particles compose it. In the case of rubidium, the fact that it has a single electron in its outermost shell, makes it vulnerable to excitation. (When an electron is unpaired in a shell, it is more loosely bound to the nucleus.) Hydrogen, the smallest atom in terms of number of protons and electrons, can be pushed into the Rydberg state by experimenters. Hydrogen, like rubidium, has a single electron in its outer (and only) shell.
One way to create a Rydberg atom is to zap it with a stream of particles such as photons, electrons, or ions. The stream can a excite single electron in an outer shell to form a larger cloud (orbital).
Large atoms created by exciting outer-shell electrons are called “Rydberg atoms” in honor of the Swedish physicist, Johannes Rydberg. In 1888, Rydberg published an improved mathematical formula for calculating the wavelength of photons emitted by hydrogen atoms when transitioning from one energy level to another.
*This experiment was by Serge Haroche and colleagues in 1996. It explored quantum behavior and was awarded a shared Nobel Prize in 2012.