The p value is that used in standard chi-square and other statistical tests. This value ranges from 0 to 1. A value of .01 suggests a 1% danger of being wrong in claiming a relationship, .05 would give a 5% danger of error. In the social sciences a 5% risk is usually considered acceptable.
Setting the p value
In the case of key item analyses, where the notion of risk combines with selectivity and strength of relationship, you may often wish to set a comparatively stringent p value threshold such as 0.000001 (one in 1 million) (1E-6 in scientific notation). A p value alone tells you nothing about whether the relationship is weak or strong, however and if you are going to be guided by BIC scores you are recommended to leave the p value at 0.1.
Alternative to p value
So it is better to set a suitable BIC score threshold such as 2.5 or greater, measuring the strength of the keyness and not just its significance.