What is meant by "society”?
Society is a long standing group of people sharing cultural aspects such as language, dress, and norms of behaviour, artistic forms and thoughts.
What is meant by the word "welfare"?
Well, welfare means health, safety, happiness, and prosperity. These are what we all want to have in our life. We want the best for our society .we want to make it a place having all these qualities.
How welfare of my society depends on my well being?
People living in the society always think that if the society changes then the other people living in it would also change. This is a very wrong thought. A class can never be called a good one until and unless all the students in it studies and behaves well. The same applies for our society and the people living in it. Unless the people start to live a life full of happiness, love, safety and prosperity, the society can never progress.

I need to change myself first. I have to be a good person and be loving, caring and helpful to others. I cannot be rude to others and expect others to be kind to me. This is not possible. We all know that, “as we sow so we reap”. If I start the change just as sowing a seed then automatically others would follow me and gradually the whole society would change and become the best one just as a big and strong tree. When other societies would see this change in my society then they would also soon try to improve themselves which in turn would improve the whole society. This is how the welfare of my country depends on my well being. 
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              "welfare of  society depends on my well being"                                       
              yeah welfare of my society depends on my well being. I agree with this but there are many people who actually don't agree with this the welfare of any kind of place may be it is a city, town or even it might be country first we the people who are staying in the society or any place should be developed. the development should be in all the aspects not only the money wise but in all the aspects on which our economy is depending. the country's development is depended on the society and the society's is on the people living in it. the society would develop only when we the people living in it are developed in all the sectors but not only in the way on money or living standards. many people say that first the society would develop and then their turn would come for development which is really a wrong estimation and I would suggest every one first them to develop and then the society would automatically would develop. hence I conclude that welfare of my society depends on my well being.
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thank u so much to mark my answer as best :)
good answer
thnx @preet2002