The knowledge of many lifetimes are captured here in this brilliant explanation of Karma by Sri Sri Ravi Shankar, many may say that they don't believe in Karma, well one may not believe in the law of Gravity, so would it stop one from stepping into the path of a falling piano?
Karma is a complicated subject, but it does make sense in a grand scale of creation, there is a underlying reason for everything, and yes, including you reading my post right now!
I picked up some gems from his video and paraphrased it according to my own understanding:
Karma is action, that results from the impressions of the mind, the action it has produced, and the new impressions it is going to produce in the mind in the future which will cause further actions. Karma is latent impressions in the consciousness, which propels you to do an action, the present action in turn creates impressions in the consciousness, which propels you to do further actions.
The impression of action, the action and its impact is all called karma, the whole universe is full of impressions. The skill is to live in karma but yet not affected by it, this is what is yoga, In the Bhagawan Gita Lord Krishna says "one who sees action in inaction, and inaction in action" is the most intelligent man. I take this as acting without attachment or ego.
To get rid of Karma, we have to get rid of these deep mental impressions. There are negative impressions which cause us suffering, we need to get rid of these, then there are positive impressions which gives us peace and joy these are ones we need to keep.
The way to get rid of negative impressions is by relaxing, pranayama, meditation or positive action. Positive impressions are like soap which washes away negative impressions, however attachment to positive impressions also turns them negative. The second step, to be free of attachment to positive impressions as well. Nirvana is when you are not attached to anything positive or negative.
Freedom does not mean stopping action, but doing it guided by your inner light and being a witness to the actions. Sri Sri Ravi Shankar compares a child's response to a vaccination shot as to an adult, in the former life is much more miserable, because one does not understand that the shot is good for oneself.
Also interesting is the mention of stored karma, present karma and future karma. Stored karma can be erased, future karma can be modified, however present karma is like a arrow leaving the bow, it is in mid flight it cannot be changed, only your attitude towards it can be changed.