# Implications and interpretation of conditional independence assumption

I am currently studying Treatment Effect Analysis and I am reading about the Conditional Independence Assumption (CIA): \begin{align} (Y_1,Y_0)\perp D|X \end{align} So the outcomes are independent of the treatment, conditional on X.

First Question: Can someone explain this better? So give a real interpretation of this and not just the mathematical formulation verbally?

The CIA implies mean independence.

Second Question: What does this implication mean? So what is the connection about the CIA and the measurement of the treatment effect?

I am not used to the topic and tried to read typical literature, but they are not really giving an intutively interpretation.

Regarding the first part of your question. I believe it is more correct to say that $D$ is an indicator for assignment of treatment. Thus the assumption is that the choice, whether an individual gets treated or not, is not correlated to possible outcomes.
If there is such non-random assignment to treatment and you know that the assignment depends only on characteristic $X$ (in this case computer literacy), you make an assumption that after controlling for $X$ both the treated and non-treated groups are equivalent in their remaining characteristics, except that some of them got treated and others not. So the difference between outcomes of the treated and non-treated can be attributed only to the fact of being treated, not that the individuals in groups were different from the beginning. Conditional on $X$ you assume that assignment to treatment is random, so it cannot correlate with possible outcomes.