What is the difference between 人民 and 民族？
人民 is translated as "(the) people". You can find it in popular expressions like:


  
  人民共和国 = People's Republic; as Huang said in the comments, if we include China it becomes "中华人民共和国"  
  人民币 = Renminbi (the Chinese currency. 币 means "money, coins, currency".)  
  人民日报 = "People's Daily" (a newspaper)
  


民族 means "ethnic group, nationality", for example:


  中央民族大学 Central University for Nationalities


All of the examples have been taken from the CEDICT dictionary.