I can just give broad outlines with only that much information. I am assuming that this is an assignment?
The first thing you need to do is decide if you agree with the statement that the welfare of your society depends on your well-being. To determine that, you need to define your terms (what is the "welfare of society" and how will we know when it's achieved? What do I mean by well-being?Health? Happiness? Survival? Religious beliefs?) Without defining your terms, any statement arguing for or against that is meaningless, because it's far too general.
Once you know what exactly you consider the meaning to be, you then decide if, going by that definition, the statement is true.
For example, "welfare of society" might mean its economic standards and its reliance on a shared set of values. (You need to decide what you think is important; these are just two common considerations.) Your own well-being you define as being physically healthy and mentally alert and well-educated; ie constantly learning.
So then you'd ask, "do I have to be healthy and well-educated for the society's economic status and/or its ability to have values in common?"
The answer to that is your essay. Remember, you can answer yes, no, or it depends quite reasonably; you just have to back up your argument with evidence.