Because of illness, he had no choice but to postpone the meeting.
Literal
Illness [because-のため] he [topic-は] meeting [object-を] postponing [had-no-choice-せざるを得なかった].
せざるを得なかった is a literary/formal expression meaning 'had no choice but to do.' Built from the classical negative ざる (= ない) + を得ない ('cannot obtain/achieve'). 延期する means 'to postpone.' The formal grammar elevates the register.