Scenario 1- If you are importing and updating an existing address in The Raiser's Edge:
Change the Address Import ID in the import file to the match the Address Import ID of the address. This can be found on the existing address record with the following  steps:
1) Open up the constituent record
2) Go to the Addresses tab
3) Select to open the specific address record that will be updated
4) Select File > Properties. The Import ID listed here is the Address Import ID, and this value needs to be entered in the Address Import ID (AddrImpID) in the import file

OR

Scenario 2- If you are importing a new address into The Raiser's Edge:
On the General tab of the import under 'What do you want to do?' select to 'Import new records' instead of 'Update existing records'

OR

Scenario 3- If you are importing new addresses AND updating existing addresses in the same import file to The Raiser's Edge:
1) On the General tab of the import under 'What do you want to do?' select to 'Update existing records'
2) Also on the General tab, find the 'Options' section and check the box to 'Import records not found as new records'
3) Verify the Address Import ID (AddrImpID) matches the existing values in the database for the records to be updated (to locate this, see the steps in Scenario 1)