What exactly do dash-to-dock intellihide and intellihide-mode dconf variables do on GNOME 3?

At least since 18.04 Bionic Beaver, maybe previously, dash-to-dock GNOME extension was defined as system default dock application and its settings are stored through dconf.

One of those got me confused. The available value description and summary couldn't help me so much, and trying to discover what it does I haven't observed any difference between turn it on or off. So I'm bringing this doubt to here!

What do org.gnome.shell.extension.dash-to-dock intellihide and intellihide-mode dconf variables do?

The intellihide key dictates whether the dock follows the "intelligent auto-hide mode". That means if you set intellihide to true, the dock would always be visible unless it's overlapped by "a window".

The intellihide-mode defines the "a window" part as mentioned before, i.e. it tells the dock which window to dodge. You can set it to avoid all windows, or the windows belonging to the currently focussed application, or only maximised windows.
You can check all possible choices by running the following command:

gsettings range org.gnome.shell.extensions.dash-to-dock intellihide-mode