Hi there,
National Insurance contributions from your salary go into the government coffers. From there, all the various public spending the government does uses the money you, and I and millions of others have put there. Partly, this will include your State Pension yes, and of course the already mentioned NHS. The Police, fire Service, teachers, ministerial salaries (and expenses - sorry !) government ministry's etc etc are all funded from here as well.
If you decide to up sticks and move elsewhere, and say you've contributed 10 years worth into it, you should be entitled to that money back in the form of a pension after what would have been your retirement age had you stayed. Once it's been paid in, it's not accessible prior to that date.
I'd suggest that you speak with a Financial advisor to at least find out a little more and of course then speak to a suitably qualfied tax advisor who has knowledge of the UK tax system (including pension knowledge) and the country you do eventually retire in (in this case sounds like it might be back inthe USA) so you can ascertain any tax implications and currency implications etc etc.
Someone has already pointed out, the UK pension amount isn't very much at all, add in to the fact theres a real mess concerning pensions from a government level, I'd suggest keeping your option of a UK pension in collaboration with other savings and investments you make for your retitrement - i.e , have some more rather than just a UK pension.
Cheers, DtM! West London & Slough UK!