What is the purpose of the Human Instrumentality Project?
The ultimate goal is to unite all the individual souls of mankind into one singular being.

This would create an existence where nobody existed individually, but as part of a whole. 

This way, the flaws in every living being would be complemented by the strengths in others, thus erasing the insecurities in people's hearts. Creating the ultimate, god-like being.

To achieve Instrumentality, the merging of Adam and Lilith, resulting in the Third Impact, is required.

Both Seele and Gendo had their own idea of instrumentality. Neither was realized.