This practical style of T'ai Chi Chuan hails from Hong Kong (Detailed lineage available on Dan's site) and has 5 aspects:

1. Dao Chuan - the slow flowing Hand Forms
2. Tui Shou - 8 styles of Solo and Paired Pushing Hands
3. San Shou - Self Defence Applications
4. Traditional Weapons - Forms and Applications
5. Nei Kung and other strength, stamina & conditioning training.

Many people only seek to practise hand forms but I introduce students to pushing hands exercises in their first class as they are fundamental to progress in the art.

Other aspects are optional but when teaching a section of the hand form I will always explain the related application. Without some understanding of the martial techniques from which they come the movements of the hand form can seem arbitrary when they do have meaning and must have focus. But again, don't worry, you don't have to do the practical applications yourself. You just need to know what they are to give your hand form some Yi or intent.