They convey approval by nodding, clapping, smiling, and sometimes bursting into laughter.

Literal

Nodding-[and-たり], clapping-[and-たり], smiling-[and-たり], also, bursting-into-laugh-[and-たり] doing-[て form] approval [object-を] convey.

A description of audience behavior. The four ~たり forms list examples of actions, all connected as parallel components. 爆笑 ('explosive laughter, loud laughing') is 'bursting into laughter'. 承認 ('approval, recognition') is a formal noun used in various contexts from audience response to bureaucratic approvals. 伝える ('to convey, transmit') is the standard verb for communicating feelings or information.