The Sanskrit word yoga means add, unite, or attach. Yoga can be defined as the link between body, breath and mind. Other meanings include endeavour and diligence.
Hatha Yoga is the most common form in The West and focusses on posture, breath and bodily health. The basic principles were collected by Yogi Swatmarama in the Hatha Yoga Pradipika in 15th century. It includes both physical and breath training with the aim of building strenth, flexibility and self-control. The 4 most common practices are:
Asana(Posture) - Balances strength and flexibility which leads to good general health.
Pranayama(Breath) - builds lung capacity, lowers heart rate and enables focus.
Bhanda(Core) - Strengthens core to support the lower back and balance.
Dharana(Mindfulness) - Alleviates stress and builds concentration
Raja Yoga focusses on mental and spiritual practices as described in The Yoga Sutras of Patanjali. Its purpose is citta-vṛtti-nirodhaḥ - cessation of the pertubations of the mind