This is a really old post, but is still the highest hit when it comes to searching google for this issue so I'll try to explain.
A code page in SSIS corresponds to the specific character encoding used e.g. ASCII is code page 1252 and UTF-8 is code page 65001. SQL Server stores character data using "Collations" corresponding to different code pages. A character encoding is the method in which characters are stored as binary data.
If you are using an OLE DB Destination where the actual destination is a SQL Server instance then you may encounter this error for several reasons.
1. Your "source" text file is UTF-8 and your destination columns are VARCHAR/CHAR datatypes. Note that most UTF-8 (99.9%) files contain unicode data so you should use NVARCHAR/NCHAR datatypes for the destination columns.
2. Your "source" text file is ASCII (code page 1252) and your destination columns are VARCHAR/CHAR datatypes but have a collation that supports double byte characters e.g. Korean_Wansung_CI_AS (code page 949), (I'm not sure if any of the SQL Server VARCHAR collations actually use code page 65001 though). If you never specified the collation when creating the table then you should check to see what the databases default collation is. You can fix the issue by altering the collation of the columns in the destination table to something such as Latin1_General_CI_AS, but I would avoid this if you can't say for certain that there isn't and won't be any non-ASCII characters stored in the data.
Be careful changing code pages if you don't know what they stand for. If SSIS automatically uses a code page of 65001 then you should not change the code page to 1252 as this will cause a corruption of all unicode data in the file, you will know this has happened if you end up with text that looks a bit like this "ã„´ã…‡ë¦¬ã…í˜¸ëŒœã…".
I've experienced many frustrations with similar issues to this, so can only hope that this post might save someone else from a little bit of pain.