次(cì) is one of the most frequently used measure words and is used to show the number of the event that happened. For example,
1)我见过他三次
Wǒ jiànguò tā sāncì
I meet him three times
‘I met him three times.’
遍(biàn) is used to describe a complete action from the beginning to the end. For example,
这个电影我看了三遍
Zhège diànyǐng wǒ kànle sānbiàn
This movie I watch three times
‘I saw this movie for three times.’
彭小川,李守纪,王红. 对外汉语教学语法释疑201例. 北京:商务印书馆,2004.