On average, I go to the movies twice a month.

Literal

On-average, month [to-に] two-times movies see [to-に] go.

月に二回 is 'twice a month' — 月 (month) + に (per) + 二回 (two times). 映画を見に行く uses the purposive ~に行く: 'go to see movies.' 平均して (on average) frames the statement as a habitual approximation.