Let's start by defining Hatha: Ha means sun and is represented by the sun of your body, your soul. Tha means moon, which is your consciousness, your mind. So Hatha Yoga is the quest for balance between the solar and lunar forces, respectively male and female. This is achieved through the fusion between mind with the soul.
One of Hatha Yoga characteristics is mindfulness. It means, if you are doing an asana (physical posture) should be fully present at all stages, which are: entry, stay and exit. If you are a practicing pranayama (breathing exercise) should be mindful breathing.
Hatha Yoga is very focused on the body work, gives a lot of attention to the correct body alignment during the asana. By breaking up body patterns, breaking emotional patterns, breaking behavioral patterns.
All of these standard breaks occur due to the fact that the physical body is aligned accurately, our breath is aligned with the same precision, then the mind, emotions and senses come into balance. As the Hatha Yoga practitioner progresses, he becomes aware of how the senses, the mind and the breath should be used to align the body. Want to understand better? It's simple, the goal is to make the asana with awareness and love. Bring in your mind intelligence to the energy of your heart and let the union of the two guide you.
There is no right age to start, children can and should practice (there are specialized instructors teach small). Anyone can do Hatha Yoga, no matter the age or sex.