Barra risk factors are particular factors used to implement the Barra risk factor analysis, that consists in a multi-factor model developed by Barra inc. to measure the overall risk to which a financial asset is exposed.
According to investopedia.com:
Barra Risk Factor Analysis incorporates over 40 data metrics
including: earnings growth, share turnover and senior debt rating. The
model then measures risk factors associated with three main
components: industry risk, risk from exposure to different investment
themes and company-specific risk.
Finally, Barra risk factors do not differ from common risk factors used by other practioners or academics from a theoretical point of view, but, rather, are a synthesis of them and of the asset risk.
I suggest to read the last release of MSCI/Barra methodology, in which MSCI explains which are the factors used and how they construct them to get a clear idea about such risk factors.