This feature is exclusive to Apple TV 4K with home theater audio mode using HomePod (second-generation) speakers. It is not offered for the original HomePod or HomePod mini (probably because the single speaker design cannot sufficiently render different output channels).
It also appears to only be available with apps that use the standard system video player. You activate it through the Sound menu above the progress bar, with the Enhance Dialogue option next to the long-standing Reduce Loud Sounds option.
Apple says enabling the Enhance Dialogue option analyzes audio being played and separates the actors’ speech from effects and background music, “bringing dialogue forward to the center channel”.
If you want to try out this feature right now, you will need to install the tvOS beta on Apple TV and install the HomePod beta (which necessitates installing a limited distribution AppleSeed profile). Otherwise, wait until the fall when these new OS’s ship to all customers.
Other Apple TV software features coming this year include FaceTime via Continuity Camera, redesigned Control Center, third-party VPN support and more.