The central aspect of Deep POV is that the narrator is the character in that exact moment of time, with all their current knowledge, emotions, and biases.
Often in writing, the narration may focus on one character at a time, but there are slight differences between the narrator's voice and the character's. One example of this would be the narrator telling the story from the perspective of already having lived through the events of the whole book. Another example would be when the voice of the narration is just a little bit more formal in tone than the character's voice. In these cases, the narration isn't inside the character's head during that exact moment of time. Deep POV tries to close this gap as much as possible.
Deep POV can be done in first or third person, but most advice about deep POV focuses on third person because that style of POV has a much wider spectrum of closeness to the POV character. Most first person stories are already in deep POV. (An exception to this rule would be the character narrating the events from the future.)
Current industry trends increasingly favor deep POV and seem to be moving more and more in that direction. Readers really connect with the characters and get invested in stories written in deep POV. But that doesn't mean it works for all genres.
Action-based stories are often focused more on the external events and can benefit from a bit of distance from the characters. Stories with mysteries can also work better having more distance from the POV characters so you don't have to dance around their secrets.
On the other hand, introspective stories often work well for deep POV. Romances, coming-of-age stories, and books with a strong focus on the main character overcoming their own flaws all may be best in deep POV.
Happy writing!