。
She was wearing clothes appropriate for the party.
Literal
She [topic-は] that party [for-に] suitable clothes [object-を] was-wearing.
ふさわしい ('suitable, fitting, appropriate') takes に to mark what something is fitting *for* — ~にふさわしい reads like 'suitable for X'. The whole パーティーにふさわしい服 functions as a relative clause modifying 服 ('clothes'): 'clothes [that are] suitable for the party'. 着ていた is past durative — she was in the state of wearing them, not in the act of putting them on. Note that 着る/履く/かぶる/する/つける all translate to 'wear' in English, but Japanese carefully distinguishes by body part and clothing type: 着る for upper-body and full-body garments, 履く for legwear and footwear, かぶる for headwear, and so on.