Post-hoc fallacy is that condition where regression shows a high degree of correlation (R square is high), but there is no real cause-effect relationship between the independent and dependent variables. For example, when the rooster crows each morning, the sun pops up every time (even if we can't see it). R square would be 1.00 in this case, but does that mean the rooster's crow actually caused the sun to rise? Clearly not, that would be post-hoc fallacy to conclude otherwise...there is no real cause and effect.
How would you explain post-hoc fallacy to your boss or CO, who has no statistical background?
In terms of explaining this to someone with no statistical background, the example in the first paragraph does a good job of this. Can you think of other instances in which there is a strong correlation (positive or negative) but no causation? For instance, ice cream sales and snow shovel ...