Elimination of features based on high covariance without affecting performance?
$|d| \gg 0$ means there is a very strong correlation between $x_1$ and $x_2$. This means one can be expressed (almost completely) in terms of the other, thus one of two is almost redundant.
A simple example:
Consider that $x_2$ is simply a copy of $x_1$, ie $x_2=x_1$. Does $x_2$ offer any new information about the the label $y$ apart from the information $x_1$ provides? No, it is clear.
Now consider that $x_2$ is simply a shifted version of $x_1$, ie $x_2=c_0+x_1$. Does it now offer any new information apart from what $x_1$ provides? Again no, by simply changing the reference point $c_0$, which is equivalent to changing the baseline of the measuring system, does not  by itself offer new information.
Thirdly consider that $x_2$ is a re-scaled version of $x_1$, ie $x_2 = s
 \cdot x_1$. Does it offer now different information than what $x_1$ provides? Again, no since scaling is equivalent to changing the measuring unit of $x_1$, but this is simply a re-naming of units, no new information is added.
One can see that any transformation of the form $x_2 = c_0 + s \cdot x_1$ does not offer any new information from what $x_1$ already provides, by the arguments above.
If one wants to be more realistic one can add some noise, ie $x_2 = c_0 + s \cdot x_1 + \epsilon$, where $\epsilon$ is some random variable with zero mean and very small variance.
A correlation value $|d|$ which is quite high actualy means that $x_2$ can be expressed as such a transformation of $x_1$, ie $x_2 = c_0 + s \cdot x_1 + \epsilon$ (or vice-versa) (there are some non-trivial exceptions to this). So $x_2$ offers no new information apart from what $x_1$ offers and is redundant.
So if such a high correlation exists between variables/features, one of them can be always eliminated without diminishing performance as being redundant (in the sense that, as far as second-order statistics are concerned, the two variables are identical).
This is one of the main rationales of feature selection and dimensionality reduction in machine learning.