1. Yoga is one of the four primary ways Hinduism guides to reach god. (For those who don't believe in "god" read it as it's one of the ways that guides to find the true nature of the "self"). The other three ways are Karma (actions), Bakthi (Devotion) and Jnana (self Inquiry).
2. Yoga is also one of the six (darśanams) orthodox schools of Hindu philosophy. Other five are Samkhya, Nyaya, Vaisheshika, Mimāṃsā and Vedanta. Yoga Sutras of Patanjali is the oldest surviving book about yoga available today. It divides yoga into eight elements/steps.
3. Yoga actually has eight elements/steps and what the world today refers as yoga is just one or two of these eight elements. All these eight steps are required to be followed in the order, one after the other (after accomplishing 1 go to 2, then 3, etc) in order to attain the ultimate wisdom.
These are the eight limbs of yoga that Yoga Sutras explain.
Yama : Practice of non-injury, truthfulness, continence, non-stealing, etc
Niyama : Internal and external purity, contentment, etc
Asanas : Body postures (What we all refer as "Yoga" today).
Pranayama : Breathing exercises, control of the "prana"
Pratyahara : Control of the senses (When a person masters and practices Asanas and Pranayama properly he gets the mental strength to control senses that's why this step comes after them)
Dharana : Concentration of the mind on an object.
Dhyana : Meditation or an unceasing flow of ideas connected with one object.
Samadhi : The meditator and the meditated become one / Union with the universe (God)
Later, "Asanas" and "Pranayama" were separately extracted from the eight elements of Yoga and put together as "Hatha yoga". This is the portion referred as "Yoga" in the present world but the actual Yoga has eight elements and Hatha yoga (What word "yoga" today refers to) is just two of the eight elements of yoga.
4. According to all ancient scriptures about yoga, main purpose of yoga is not merely an exercise for body. Yoga is an art of awakening the super natural energy dwells within man by awakening the "Kundalini" power. Kundalini power is stationary in the bottom of spine and the purpose of yoga is to bring it to the top of the head. As "Kundalini" rises man gets many subtle and supernatural powers. Extrasensory perception, Telepathy are some of the example super natural abilities that awakening of "Kundalini" brings. (Note, that yoga is not the only way to awake Kundalini but, yoga is the most known way for awakening Kundalini). Once Kundalini reaches the top of the head (Sahastra Chakara) man attains the ultimate bliss and merges with the universe (union with god/self realization).
5. There are no complete scientific explanations for many of the mental and obviously spiritual achievements accomplished by yoga. Yoga and the fruits of hata yoga are one of the evidences that ancient civilization discovered techniques that can not be fully explained by today's science.
6. Yoga does not have any bad side effects when they are done as prescribed. There are hundreds of positions (Asanas) and not a single one has any side effect. But most of the modern exercises such as gym have their own bad side effects in a long term. Pretty amazing right?