。
She applied what she learned in class to the experiment.
Literal
She [topic-は] class [in-で] learned [nominalizer-こと] [object-を] that experiment [to-に] applied.
応用する (おうようする) means to apply or put into practice — taking theoretical knowledge and using it in a concrete situation. 授業で学んだこと (what she learned in class) uses a relative clause + こと to nominalize the learning. The に marks the target of the application — the experiment where the knowledge was put to use.