There is a wealth of literature on the nature of protein structural similarities,
and this manual is not the place to review them. If you want to look into
the subject, then I would refer you to some of my papers [11,13,14]
and references therein.
An important aspect of assessing the meaning of structural similarity is discerning whether a similarity between proteins in the absense of obvious sequence identity implies a common evolutionary acestor, and usually an associated similarity in molecular function. Some studies have found that it is possible to discern homology by the analysis of the sequence identity calculated following protein structure alignment. Note that this is a very different identity than that quoted during typical sequence comparison (e.g. BLAST, FASTA, SSEARCH, etc). During sequence comparison, the reported % identity is the result of optimising the alignment of two sequences, thus numbers as high as % 20-30 are possible for proteins that are definitely not homologous (i.e. those having different tertiary folds). However, if an alignment has been derived without consideration of the amino acid sequence, then lower % identities can still be significant. See Russell et al. , 1997, and Murzin, 1993 for examples, and more details.
STAMP reports both the % identity from structure comparison, defined as the precentage residue identities (m) within structurally equivalent residues (n), and an estimate of the statistical significance (reported as P(m)) of a given a particular combination of m and n. The latter is described in Murzin (1993). Values of P(m) smaller than about 10-3 very often indicate that the pair of proteins are within the same protein superfamily, which implies a common ancestor, and more importantly very often indicates a similarity in molecular function. Specifically, the P(m) is calculated for a p = 0.1; please see Murzin (1993) for a more through explanation of this calculation.