。
She explained that she couldn't attend the meeting.
Literal
She [topic-は] meeting [in-に] cannot-attend [quotative-と] explained.
Same indirect-speech machinery as the typical reporting-verb pattern: an embedded clause + the quotative と + a verb of communication, here 説明する ('to explain'). 出席できない is the negative potential of 出席する ('attend, be present at'), more formal than the everyday 出られない. The whole sentence reads in the careful register of a workplace email or message left with a secretary — explaining the reason for an absence rather than just noting it.