There are many proven benefits of Yoga And Meditation. Meditation helps calm and clear the mind, developing clarity of thought whilst easing anxiety. Yoga helps soothe the nervous system, detoxes the cells of the body, eases stress and relaxes you.
Yoga and Meditation are frequently combined as they are very complementary disciplines. Meditation is frequently part of yoga classes as a way to relax and focus the mind after holding asanas.
Meditation is a hard skill to master. It's not just sitting doing nothing! To be in a medative state you must try to clear the mind completely. It's very easy to find yourself thinking about things (like thinking about how not to think about anything!). Meditating for extended durations becomes harder as the mind starts to wander. Some people find it easier to listen to some calming music whilst meditating as this helps anchor the mind and stop it drifting.
Practicing Yoga and Meditation should be done under the supervision of a qualified teacher who can ensure you are performing both activities properly.