So if a slope is deemed insignificant I understand that tells us that specific independent does not help explain variance of the dependent. But, what does an insignificant Y intercept tell us?
nothing. you could have a line pass thro the origin, can’t you?
Normally you wouldn’t test for significance of the intercept. Generally speaking it is important that you keep the constant in a regression model otherwise your predictions become biased. That aside, an insignificant Y intercept means that it is not significantly different from zero and it’s meaning will need to be interpreted in regards to the data used and the problem at hand.