Buddha
Siddhartha Gautama, who was born in the royal family, had left the wealth and luxury life after He seen the birth, old, sick and holy man. Gautama believed that life is full of samsara(pain) as we are in the cycle of life(re-birth) that need to be ended to reach true hapiness. At the age of 29, He started to experience all different method to find the true happiness and at the age of 35, He finally reached to 'Enlightenment', and spend the rest of His life to teach Dhamma(also known as the Buddha's way). Buddha and dhamma soon then became one of the major teaching.
Buddhism
Buddhism goes beyond religion and philosophy, the basic teaching is the 'way of life' to reach to the real happiness. After more than 2500 years of Buddha's life, Buddhism is practiced by about 370millions people around the globe up to date. Dhamma teaching is based on 'middle' way, Buddhism shouldn't be too extreme or too weak in everything, it need to be moderate.
Karma
Every action is called Karma, whatever we done, whatever will happened to us, if we do good karma, we will receive good return and same to opposite. Based on the law of cause and effects, karma(good or bad) might happened in our present, next life or next's next life or so on.
A quick introduction to 4noble truths in Buddhism
1. Life is suffering, the proved is pain, old, sicknesses and death.
2. Life suffer because of craving and lust.
3. Suffering can be ended and true happiness can be attained.
4. 8 fold path is the answer to end the suffer and attain happiness.
Siddhartha Himself reached 'Enlightenment' by focusing on the real truths, meaning that only our-self can help our-self to reach the true happiness or Nibbana(end of re-birth). Buddha teaching us the way, Dhamma provide us the practice code, Sangka(monk) as our guide.
Sadhu Sadhu Sadhu