So you backup a database from 'server a' and then move move the backup file to 'server b' and restore it.

Unless you restore the system databases as well the logins from 'server a' do not follow to 'server b'. So you have users in your database after it is restored but the logins that are mapped to the user are lost. You will need to recreate these logins on 'server b' as they are on 'server a'.

http://support.microsoft.com/kb/314546 -- check out step 2.