during next week; sometime next week; throughout next week
Refers to an action or event taking place within the timeframe of next week. The exact interpretation (at some point vs. throughout) depends on context.
Please submit the report sometime next week.
It seems it will rain throughout next week.
Simply means 'next week' without the 'within/during' nuance.
Compound of 来週 (next week) + 中 (within/during).