This out of context clip completely misrepresents the talk - I highly recommend you watch the whole thing:
http://www.youtube.com/watch?v=JaF-fq2Zn7I
Bill Gates is describing the effect of taking a population out of poverty - the combination of vaccinations, health care and specifically reproductive health services. Bill is simply pointing out that in a population where women have some control over their reproductive cycle and children aren't likely to die of preventable childhood diseases, poverty and unsustainable population growth both start to fall away.
This is not a revolutionary idea: http://www.youtube.com/watch?v=EZ0K0rEsR0M
The whole debate (and subsequent conspiracy theories) over vaccines was started with a fraudulent paper from Andrew Wakefield in the UK. Further reading:
