I know vinyl is analog, but what does that mean, exactly?
Analog means that there is a continuous signal in which the varying part of the signal is a representation of another time-varying quantity. So, when it comes to sound recordings, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. Basically, the groove of a vinyl record is like a drawing of the sound wave in a single continuous line through the entire side. Your turntable essentially reads that and decodes it in real time, which results in the sound you hear from the speakers.