National Insurance: What is it, what does it fund and what happens if it’s scrapped?

In his Spring budget, Chancellor Jeremy Hunt confirmed a 2p cut to workers’ National Insurance. This indicates the government’s eventual ambition to scrap the tax entirely.
Well, National Insurance acts as a form of social security, and is defined by the Oxford Dictionary as being the system of compulsory payments to provide state assistance to people who are unemployed, poorly or retired.