Pillars of Eternity stores its save games in the following locations:
%USERPROFILE%\Saved Games\Pillars of Eternity
%USERPROFILE% usually is something like C:\Users\your-name-here
For Steam, GOG, and DRM-free backer disc versions:
~/Library/Application Support/Pillars of Eternity/Saved Games
If you bought Pillars of Eternity from the Apple App Store, your save game directory is located here:
~/Library/Containers/com.mpdigital.pillarsofeternity/Data/Library/Application Support/Pillars of Eternity/Saved Games
If $XDG_DATA_HOME is not defined, it's stored in ~/.local/share
There is one other folder that you may find in your temporary locations where we build and maintain the current game state, but this is not intended to be shared / used if you go to play on another machine.
For the Backer Beta, save games were stored in non-standard locations, such as roaming or temp folder locations. Those were changed for the final game release.