When analyzing a character, there are many factors to be taken into account.
Types
Characters can be round (multi-dimensional, complex, with strengths and weaknesses) or flat (one-dimensional with only a few surface traits)
Development
We call a character's journey and their transformations a character arc. However, there are static characters that don't change and dynamic characters who evolve.
What to look out for
When analyzing a character, it is helpful to look at their motivations, struggles, reasoning, relationships with others and motives.
Revealing a character
The author chooses how they want to reveal a character. Through direct or indirect characterization, dialogue, actions, thoughts and interactions.