。
She often listens to records for hours on end.
Literal
[topic-は] often many-hours [emphasis-も] records [object-を] is-listening.
何時間も is the standard 'for many hours, for hours and hours' construction — the question word 何 ('how many') plus a counter (時間) plus も creates an emphatic 'lots and lots of [unit].' Compare 何度も ('many times'), 何冊も ('many volumes'), 何百人も ('hundreds of people'). The ~ている form here is habitual rather than progressive — describes a typical pattern of behavior, not a current moment of listening.