The day, week, month, etc. before last
Definition 1 of 1
Pro Tip 1/3Past Events
Used to talk about events that happened two time periods ago. 
He left the city the day before last.
Pro Tip 2/3Not Yesterday
It does not mean the most recent past period, but the one before it. 
The festival took place the week before last, not last week.
Pro Tip 3/3Time Clarification
Sometimes used for clarification when 'last' could be confusing. 
It rained the Monday before last, not last Monday.