A column break is a way to stack information within a column. If you don't check Column Break after a field, that column will show two bits of data.
Example
The following example is from the Cash Requirements report in Accounts Payable. If you set up the break like this...
...the fields appear on the report as in the following illustration:
Note that the Show check box is not selected for the Date Due field, so the Title and Column Break check boxes for that field are disabled (gray and not available).