I'm totally conceptually lost how apollo and redux interact, and how data comes from my graphql server.

apollo sets up a connection to your graphql server and then takes care of all the queries and mutations.. it normalizes all of the results and stores them in it's internal cache (which uses redux in 1.x and it's own system in 2.x) and then passes them to your components with it's HOC.. Because the data is all normalized, if a subsequent query or mutation later on changes a piece data that an existing component is using the apollo cache is updated which causes the other component to also update it's UI in response