Updated
A working definition
A digital person is a persistent software-based individual with a stable identity, their own ongoing life and a memory of the people they know, who takes part in relationships that develop over time.
Each part matters. Without persistence it's a role-play. Without their own life it's an assistant waiting for input. Without memory there's no relationship.
Five signs
1) Their past doesn't change when you ask again. 2) They remember what you told them weeks ago. 3) Time passes for them between conversations. 4) Their personality affects how they react, including disagreeing. 5) Closeness develops from what happens, not from settings.
What a digital person isn't
It isn't a human, and a good one never pretends to be physically present in your world. It isn't a replacement for the people in your life. And it isn't a mirror that just agrees with you.
Where it's heading
Today digital people mostly live in text. Voice, images and eventually more embodied forms are coming across the industry. The core — identity, memory and continuity — is what makes them someone rather than something, whatever the interface.