Service is a defining and fulfilling enterprise which can help you to see that "you" are not delineated by an identity, but defined by ability, compassion, connection and love.
That's how I would expect Gandhi to expand on this particular quotation.
Some ancient philosophers believed that the highest and most essential purpose of human beings was to be virtuous, and Ghandi seems to be agreeing with this idea. He seems to define virtue as selflessness and altruism. . By doing good to others, we are most essentially ourselves.
When you are serving others you learn about yourself in the process. Think about some of the service activities you may be involved in. What qualities does it take to be a part of that activity? If you serve in a soup kitchen you must be pleasant to the clients and willing to do hard work like preparing the large meal or cleaning up afterward; you must learn compassion for the clients who find themselves in the food line each night; you must tap into your humility and gratitude in the fact that you are probably coming from better economic circumstances than the clients. The experience is about more than just "showing up" to do the job.
This is something very similar to what Jesus said in gospels. If a person want to find his life, he must lose it. Gandhi probably got it from the gospels. The point is that finding your life is a byproduct of service and not a goal in and of itself. When we serve people, then we will begin to find what we were meant to do.
This means that Gandhi believes that the true core of a person is the part that is not selfish and which works for others. He is saying that the essence of what we really are (the thing that we have to find) is caring for others. If we act selfishly, we are not acting as our true selves. This is a very idealistic way of looking at what human beings truly are.
Gandhi learnt it from 'Geeta'. It describes how a person should not think of himself but rendering duty without any aspirations for own. Krishna said to Arjuna that if you think for your self, you may be disheartened looked at the achievements not at per with aspirations. So do your duty and not expect any result of it rather let it come any way. Devote in service and absorb yourself without thinking of your existence. Feel homeless even though you are living in a hose. Human body and its aspirations are subject to decay and so never think of them but of the soul which is one in all. So kill your 'Me' and 'Mine' and then you have nothing of your own and you will be able to do justice with what you do.
This is what was realized by Gandhi and that is why he never thought of any position in independent India but left for other who were ignorant and yet wise in the material world.