。
She was happy to be introduced to him at the party.
Literal
She [topic-は] party [at-で] him [to-に] was-introduced-and was-happy.
紹介された ('was introduced') is the direct passive of 紹介する; the て-form 紹介されて links the introduction to the resulting feeling うれしかった ('was happy'). This ~て structure is typical for cause-and-feeling sequences: 'doing X / X happening, (as a result) felt Y.' で here marks the location of the event (パーティーで, 'at the party'), and に marks the person to whom she was introduced — Japanese keeps the agent (the introducer) implicit and unmentioned, since the focus is on the experiential outcome.