What is the National Insurance in UK for?

Basically it is linked to social security payments in particular of contributory benefits where the amount you have payed in and the length of time you have paid in for alter the amount that is paid to you as part of the state pension.

Other benefits that depend on NI contributions include Contribution based Jobseeker’s Allowance
Incapacity Benefit
Widowed Parents’ Allowance
Bereavement Allowance
Bereavement Payment

Or… to put it another way it is a stealth tax where the government can increase the amount they tax you while still being able to claim that they have not increased income tax.

Adding to the question, when will i be able to withdraw that money? It is only when i reach a certain age?

You can claim your pension when you are 65.
Incapacity benefit if you are incapacitated (ie unable to work due to ill health).
Jobseekers allowance if you are unemployed.