As you can find in the doc:

in a dark theme the elevation overlays are semi-transparent white
(colorOnSurface) overlays that are conceptually placed on top of the
surface color.

It is managed by the library.
Just an example with a MaterialCardView with app:cardElevation="4dp" and app:cardElevation="8dp".

Light mode:

Dark mode:

The overlay is based on the colorOnSurface defined in the app theme.
You can change this color adding in the app theme:

<item name="elevationOverlayColor">@color/...</item>

You can also disable this behavior using in the app theme:

<item name="elevationOverlayEnabled">false</item>

Many components in the Material Components Library support elevation overlays in dark theme but you can also apply it in your custom view using using the MaterialShapeDrawable.

For example you can use a LinearLayout:

LinearLayout linearLayout1= findViewById(R.id....);
MaterialShapeDrawable shapeDrawableLL1 = 
MaterialShapeDrawable.createWithElevationOverlay(this, 4.0f );
ViewCompat.setBackground(linearLayout1,shapeDrawableLL1);

LinearLayout linearLayout2= findViewById(R.id....);
MaterialShapeDrawable shapeDrawableLL2 = 
MaterialShapeDrawable.createWithElevationOverlay(this, 16.0f );
ViewCompat.setBackground(linearLayout2,shapeDrawableLL2);

I came across elevation overlay several times. Even though I read some definitions, I seem not to find exact meaning of it. Can you help me with that? What is it? How is it used?

Here is the link