Can someone provide a valid definition or explanation of the concept "significant main effect"?...?

I am not a lazy student or an inept practitioner, but I have to read a lot of social science literature and keep running across this phrase. I am long out of school and this didn't come up in my required psych course. I have not been able to find a clear explanation of how a "significant main effect" is established or supported by data. From context I have begun to get the feeling that researchers report a significant main effect when none of the tested hypothesis are supported ... ( I know that sounds cynical - but it is just an impression) and I still don't know where is comes from statistically or in relation to the study design. Can anyone explain, especially anyone with some credentials or a cited source?