She read his letter over and over again.

Literal

She [topic-は] he [from-からの] letter [object-を] [many times-何度も] [many times-何度も] read.

Reduplication of 何度も ('many times') intensifies repetition — emotional, almost obsessive re-reading. Japanese tolerates this kind of full-phrase doubling for emphasis (cf. どこもかしこも 'everywhere,' いろいろなことをいろいろと 'all sorts of things in all sorts of ways').