Translation:I know what you read last summer…
Well, for me (native speaker) it is a difference. If we are in August now, and I say: "... det du läste i somras" will be this summer 2015, but if I say: "... det du läste förra sommaren", will be the summer of 2014. So: "i somras" = the closest summer we can think of, but "förra sommaren" is always about last year.
You are completely right. "Läser" could also mean that your taking courses in a specific subject. For example, Jag läser ekonomi would mean "I study economy.
Usually "läser" needs an object in order to have this meaning. In this case "läser" is used intransitively, and therefore it seems rather weird to assume that we're talking about courses.