The alignments of query against the templates are ordered by the p-values of the raw alignment scores. The first alignment is the most significant one. The p-value of an alignment score S between a query and a template represents the probability of getting an alignment with score of at least S in the comparison of the template sequence against a "random" sequence of an "average" length and composition. We consider the alignment scores having p-values below 1E-5 statistically significant. Those alignments are almost always "biologically meaningful". The p-values between 1E-5 and about 0.01 are considered borderline cases. However, in some instances, the top scoring alignments with p-values in this range often represent true sequence relationships.
Poleksic,A. (2009) Island method for estimating the statistical significance of profile-profile alignment scores. BMC Bioinformatics, 10(1):112.