The pattern {noun} *after* {noun} is a common rhetorical device.

> The pain came in wave after wave.
>
> We were having a great time at the pub, singing song after song.

You can think of it as a periphrasis for the plural that conveys the sense of "many" and "repetition" or "continuousness".

Paraphrases of the above:

> The pain came  repeatedly in waves.
>
> We were having a great time at the pub, singing many songs over the course of the evening.