SQL Server updates the timestamp column of a row whenever the information in the row is changed. It'll have no effects on performance unless you're accessing the timestamp column within your queries. Many developers use the timestamp to implementing optimistic locking. If the timestamp has a different value when you go to write the new data then it had when you read the data, someone else has made a change.
How are you trying to copy the tables? You can't explicitly place a value into a timestamp column. Try changing you copy routine to only place values into the columns that aren't timestamps (and identities).
-Mike