I've just started to read about elliptic surfaces in algebraic geometry.
Here's a quote from wikipedia:
An elliptic surface is a surface that has an elliptic fibration [...] such that almost all fibers are smooth curves of genus 1. [...] This is equivalent to the generic fiber being a smooth curve of genus one.
I'm trying to understand what "generic fibre" means here.
I've found some other text which mentions some "fiber over the generic point", so I guess this must be the same thing (but I still don't know what it is).
So what's the precise definition of "generic fiber"? Are there any concrete, explicit examples?
(by the way, I have some background in algebraic varieties, but I'm still crawling my way into schemes)