What it means
The Heart center is a motor for willpower, value and promises. When it is the authority, the right question is simple: do I want this, and is there something in it for me? Human Design treats that as healthy, not selfish. A commitment made from the Heart tends to be kept, and one made without it tends to be broken. There are two kinds. Ego Manifested authority (Manifestors) has the Heart connected to the Throat, and you hear the answer in what you say. Ego Projected authority (Projectors) has the Heart connected to the G center, and the answer often comes out when you talk about it with someone you trust.
How to use it
Listen to what you actually say when the choice comes up, especially the words "I want" or "I will". If you have to push yourself to want something, that is a no. Promise only what you have the will to deliver.
Who has it
Only Manifestors and Projectors can have Ego authority. The Heart has to be defined, and the Solar Plexus, Sacral and Spleen have to be undefined.
Common mistakes
Making promises you don't have the will to keep, feeling guilty for asking what's in it for you, overriding your wants to please people, and proving your worth through effort.
How Cosmic Array reads it
Your authority depends on which centers are defined in your bodygraph. Cosmic Array works that out from the positions of 13 bodies at your birth and again about three months before it, calculated with the Swiss Ephemeris, and shows your authority next to your type, strategy and profile in the Architect blueprint. The Moon moves fast, so a birth time helps. Without one, the blueprint uses noon and marks the result as approximate.