nutNhoney wrote:

My potatoes bloomed and now there are round berry like things where the
blooms were. What are these?

They are potato berries, inside of which are the potato seeds.
If you harvest your own and try to grow them you will get very uneven
results.
However, more and more true potato seeds are becoming readily
available. Google True Potato Seed for more info.
We've grown a variety called Gilroy for the last few years with
surprising results. Very slow growth for the first month to 6 weeks
but, they really speed up after that with a good yield of nicely sized
potatoes.

Ross.