LAST_N_DAYS:20

This clause means LAST 20 Days.

Using this in a SOQL Query to fetch the List of Cases created 30 days ago, the query will be 

List<Cases> allCases = [Select Id from Cases where CreatedDate >= LAST_N_DAYS:30];

THIS_WEEK

This clause fetches records created this week. The Week is calculated as per the notes from Salesforce as :Starts 12:00:00 on the most recent first day of the week before the current day and continues for seven full days. First day of the week is determined by your locale.

List<Cases> allCases = [Select Id from Cases where CreatedDate < THIS_WEEK];

More Links and methods:

Apex Date Filters: http://www.salesforce.com/us/developer/docs/officetoolkit/Content/sforce_api_calls_soql_select_dateformats.htm 

List View Filters: https://help.salesforce.com/apex/HTViewHelpDoc?id=custom_dates.htm&language=en