Boolean-based SQLi involves monitoring changes in responses to see if a query has executed or failed. The only reason you’d generally do this is if you’re doing SQLi blind (where you don’t get any output, or the output you do get isn’t strongly coupled with the input query).
Obviously, this requires that either the HTTP response code or payload changes depending on the results of the injection… (Some frameworks try to make blind SQLi difficult by using redirects, but it’s possible — though a pain — to get around this with Burp Suite).
One way this can be useful more generally is by using something like AND (SELECT COUNT(*) FROM table_name) > 0 to probe for the existence/use of table_name.