The red section is generally termed "the hitbox" and the green section is generally termed "the hurtbox". These sections, when overlayed over a character's sprite/model, show you a visual for hit detection.
A hitbox is the effective area an attack has once it is active. It may change over the course of an attack. Sometimes the hitbox may be larger than the sprite itself will show in-game. The general rule: the larger or longer hitbox, the better.
A hurtbox is the effective area in which a character may be hit. This not only applies to attacks, but also standing/crouching/running/jumping/etc. The general rule: the smaller or shorter the hurtbox, the better.
What you learn from this is the range and utility of your character. If a character is beating you consistently with normals, it may be that their character's hitbox is large enough to overlap your hurtbox without theirs being compromised (this is also what causes counter hits). For example, good anti-air normals are generally notable for shrinking the player's hurtbox while still retaining a large hitbox.
That said, some people believe there is no such thing as "priority" on moves; only properties, hitboxes, and frame data.
