How to back up only the files that changed
After a first backup, choose Only files changed since the last backup in Burn by Zaweba to put just new or changed files on fresh discs.

Once you've made a first backup with Burn by Zaweba, open the same backup set and choose Only files changed since the last backup. Burn then puts just the new and changed files on fresh discs. The index on those discs points the unchanged files back to the earlier discs, so a restore still finds everything.
This is what people usually mean by an incremental backup. It saves blank discs and time, and it makes regular backups far less of a chore.
Why it's worth doing
A full backup of a big photo or document folder can take several discs. Doing that every month would mean burning almost the same files again and again. In most folders only a small part changes between backups: this month's photos, a handful of edited documents. Burning just those keeps each backup quick and cheap, and it's more likely you'll actually keep doing it.
Doing a changes-only backup
Start from the home screen, where Burn shows each saved backup set as a chip. The set remembers its folders, the file kinds to include or leave out, whether hidden and system files are skipped, and the disc size. You'll find the saved sets in %APPDATA%\Zaweba\Burn if you ever want to see where they're kept, and Settings has a button to open that folder.
Open the set you used before and choose Only files changed since the last backup. Burn compares what's in the folders now with what the earlier backup holds, and plans discs for the difference. If the changes fit on one disc, you'll be asked for one. If they don't, Burn plans several, numbers them and asks for each in turn.
As with every backup, each file is fingerprinted with SHA-256 before burning and read back afterwards to check it, unless you've turned off Check every disc after burning in Settings. Leaving it on is wise.
Restoring across several backups
The clever part is in the index. When you restore, Burn needs to know where each file lives. A file that hasn't changed since the first backup is still on the first backup's discs, while a file you edited last week is on the newest one. The index on the new discs records this, so Restore from backup discs can ask you for the right discs across backups, join any split files and check each file against its fingerprint as it goes.
In practice that means you should keep the earlier discs. A changes-only backup isn't a complete copy on its own. It builds on the first one, so the set as a whole is your backup.
Habits that keep it reliable
Label every disc as you go. Burn offers labels and covers after a backup, with a label per disc, so the discs from each run are easy to tell apart. Keep all the discs from one set together.
Check the backup log now and then. It lists every backup with the date, the set, the discs used, the number of files and whether the check passed, and it can be exported as CSV. A glance tells you when you last backed up and whether anything failed.
Every so often, it's sensible to start a fresh full backup of the set. A long chain of changes-only backups works, but a new full copy gives you fewer discs to find when you need to restore everything at once.