Amino acids more complex than alanine have degrees of freedom within their side-chains that involve torsion angles (or dihedral angles) through the various side-chain covalent bonds. Amino acids with more than one non-hydrogen atom in their side-chain will have at least one of these side-chain torsions by which the positions of the atoms beyond Cβ are characterized.
The simplest amino acids that have side-chain torsions (ignoring hydrogens) are serine and cysteine, which have two atoms (Cβ and O for serine, Cβ and S for cysteine) beyond Cα. Therefore the position of the O or S in these side-chains are fully defined by the torsion angle through the Cα-Cβ bond. For the more complex amino acids, there are at least two torsions that are required to fully specify all the non-hydrogen atoms in the side-chain.
It was realized early in the study of small peptides that there are certain values of these side-chain torsions that are found frequently and others that are rare. The reasons for this preference for particular values are avoidance of steric hindrance (collisions between atoms) and electrostatic repulsions or attractions. For the simple case of cysteine and serine, the preferred values of the one side-chain torsion angle, denoted χ1, are 64°, -65° and 178°; these provide the maximum separation between the oxygen or sulfur and the other atoms of the amino acid. We describe these three preferred orientations of the side-chain as preferred "rotamers", and we describe the list of preferred orientations for amino acids of this kind as a "rotamer library".
For more complex amino acids there are at least two adjustable torsions, and typically there are two to four preferred values for each of those torsions, giving rise to a list of preferred rotamers. Isoleucine has two torsions (Cα-Cβ and Cβ-Cγ1, labeled as χ1 and χ2), and there are a total of seven preferred orientations for isoleucine side-chains, each with characteristic values of χ1 and χ2. Therefore the rotamer library for isoleucine has seven members. The seven rotamers for isoleucine are not equally probable: the most common is found in 60% of all isoleucines in high-resolution structures, the next-most appears 15% of the time, the next is 13%, and so on down to the sixth and seventh rotamers, each of which appears only 1% of the time. Similarly, the first rotamer for serine (χ1 = 64°) appears 48% of the time, whereas the second rotamer (χ1 = -65°) appears 29%, and the final one (χ1 = 178°) appears 22% of the time.
In real structures there will typically be a few amino acids whose side-chains do not orient themselves in the positions defined in their rotamer libraries. Often these anomalous rotamers will appear where the amino acid is strongly influenced by its environment, e.g. lysines on the surface of a protein whose orientations are influenced by hydrogen-bonding to neighboring molecules. But in a well-refined, high-resolution structure there are typically fewer than 2% of the residues will have anomalous side-chain orientations, i.e. values of χ1, χ2, ... that differ from any of the rotamer library values by more than a few degrees.
Structure-fitting programs like Coot know about rotamers and rotamer libraries. In Coot, if you click on the "Rotamers..." button on the Model/Fit/Refine menu and click any atom of an amino acid in the structure you're currently analyzing, a menu will appear that lists all the rotamers for that amino acid type. For each rotamer it will list the values of the various χ angles and the probability of finding that rotamer. This can help guide you toward placing your amino acid in electron density such that its orientation is consistent with those found in well-refined, high-resolution structures.