Socialism is a economic system in which there is equal public ownership of industry and the social systems which support the culture by the people themselves. In this system everyone is equal and receive equal benefits. In theory the goal is to reduce suffering and increase success among everyone within the society equally. A benefit of this type of economic system is that the well being of each person is a primary focus.
Capitalism as an economic system in which private ownership of industry is the primary focus. One person, or a group of people, can own the means of producing goods and profit off of this production without sharing the benefit of this production with society as a whole. The focus here is each person increasing personal benefit instead of equality of society as a whole. A benefit of this type of economic system is that one is rewarded for their own hard work and gains the full benefits of their labor.