What do 'Salaam Alaikum!' and 'Alaikum Salaam!' mean, please, guys?

Only, I heard my ex-brother-in-law and his family, (who, for the record, were from Pakistan), use these phrases all the time. Say, for instance, HE'D say: "Salaam Alaikum!" to his dad, then, his dad'd reply: "Alaikum Salaam!" What do these phrases mean, though? I'd REALLY appreciate YOUR angles on this one, please, guys. Much obliged! Peace and love! Be lucky! :)