The idea of manifest and latent functions comes from the sociologist Robert Merton. Merton argued that things like education have manifest functions (the ones that the participants are aware of) as well as latent functions (ones that they are not aware of and which may not be intended).
In education, the manifest function is to learn skills and gain knowledge. Students know that they are trying to do this. They know that they are trying to learn how to do algebra, for example.
However, education may also have other functions, intended or not. For example, education may bring about more inequality in a society. Those who get more and better education become the elite while those who do not fall further behind. No one really intends this and students are not aware of it, so it is a latent function.
You can also argue that a latent function of education is to socialize us. It is partly through our educational that we learn the values that our society wants us to have. We learn, for example, to compete with others to try to be the best. This is a characteristic of a capitalist society but it is one that we are not aware that we are learning as we go through school.