Allow me to help. Basically, the confidence interval of a parameter are the endpoints of an interval or range that the parameter can reasonably achieve. So, if 95% of the time a parameter is greater than -12 and less than 12, then it could also be zero. And, if it can be zero then it can be worthless. For example, if $A X$ can have $A=0$ then its contribution is not significant to a regression. If we had 95% CI's for $A$ of 12 to 24, then it is not likely to be worthless as it is significantly not zero. Mind you, not significantly different from zero is not necessarily an insignificant contribution, and if we had more data, it might become significantly different from zero. It is a fine point, perhaps, that not significant does not mean insignificant, and just because we do not obtain significance as a result proves nothing special.
However, that does not mean that because we have a not significant result that it is also meaningless. It does have a meaningful context, and indeed one in which the confidence intervals contribute more than a probability alone would.
Suppose we have 95% confidence intervals for $A$ as above that only extend from -1 to 1. Then they are 12 times lesser in range than the -12 to 12 CIs we had before, above. What that implies is that we would then know that a result of -5 or +5 would be significantly non-zero so that we now have a greater certainty of where the values of $A$ are not-located, and a narrower range of where our uncertain values of $A$ reside.