After finding formal definitions in various texts, I have ($I$) not been able to obtain a good intuition for them and ($II_1$) have not seen anyone relate such factors to more commonly understood Hilbert spaces such as $L^2(\mathbb R)$. This is very likely for good reason, but it would be nice to have these ideas come down from the clouds so that one can present them to non-mathematicians and (maybe this is too ambitious) laypeople.