Like Tom, I too think the explanation in Books Online is very unsatisfactory. So I did some tests to check a few of the issues.
In this specific question, two things are at stake: truncatiing a string (both on assignment to variable and during insertion in a table) and implicit truncating to integer.
String truncation: With ANSI_WARNINGS OFF, this is always accepted, with no error or warning message. With ANSI_WARNINGS ON, truncation on assignment to a variable is still accepted, but truncating when inserting to the table generates an error message and causes the statement to fail. Changing the ANSI_WARNINGS to ON in the query posted in the question will result in this error message, and the SELECT runs and shows only the column headers (as there is no row inserted).
Numeric truncation: Truncating the number as part of the conversion to integer is always allowed and will never generate a warning or error, regardless of the ANSI_WARNINGS setting.
According to Books Online, two other issues to beware of are division by zero and arithmetic overflow.
Division by zero: Any attempt to divide by zero will always cause an error. With ANSI_WARNINGS ON, this aborts the statement, but allows the rest of the batch to continue. So if the error takes place in the SET, the SET will not be executed (variable is still NULL), and the INSERT executes (inserting a NULL value). If the error is in the INSERT itself, no row is inserted.
Arithmetic overflow: Same behaviour as division by zero.