This is how "deep" a character is. It involves questions like why the character does what the character does, what the character thinks, feels, desires, and hates, backstory, and/or how the character sees the world. It may be there in Sub Text, but it still affects the depth of the character.
Keep in mind that not all characters have to be three dimensional, nor is there necessarily something wrong with a character who is not. The genre, audience, plot, and role of the character affects the minimum depth needed for the character to maintain Willing Suspension of Disbelief. Go at least that far, and you're good with the audience.
The Three Dimensions can be thought of thus:
Height: How important the character is to the story/society/main character. Most one-dimensional characters are defined by this and one or two character trait(s).
Breadth: Variation within a character. The amount of different traits that define them and how well these interact.
Depth: How the character changes the better you know them. If your ogres are like onions, they do indeed have depth.
You can go further, it's just optional. Related to this is whether a character is Dynamic or Static, these can maintain or increase the dimensions of a character, or simply "move them sideways" to change their nature without adding depth. Related to Character Calculus, at least in that the farther away a character is from the POV or Focus axes, the less developed they are likely to be.
Only One Dimension Needed
- It's a victim of The Virus, like a zombie. Unless one zombie has a major role, what more do you need?
- An extra in a crowd.
- A Mook in most Video Games.
- Cannon Fodder, unless the show is focusing on the horrors of war.
- Any character in a game with an Excuse Plot.
- A minor character in a story told to little children. Not that kids can't understand character depth. Just that they are likely to give that attention to major characters.
At Least Two Dimensions Needed
- A Virus victim in a major role.
- Most victims in a Slasher Movie.
- Minor characters in most movies.
- Major characters in a B-Movie.
At Least Three Dimensions Needed
- All but the smallest roles in a character study.
- Most major protagonists and antagonists.