Time Machine has no problems deleting older incremental files to make room for backups of new incremental files. The key word here is "incremental", which are small files that take up very little space.
But.....and this is a big BUT......if the Time Capsule drive is full, and you try to back up a larger amount of data than normal......which can happen if you have recently updated the operating system on your Mac, or added larger media files or other types of files to the Mac......then Time Machine balks, because it cannot delete enough of the older files to make room for the new, larger than normal backup.
In that case, you have a few options:
1) Add another Time Capsule and start new backups going there
2) Add a USB drive to the current Time Capsule and start new backups going there
3) Erase the Time Capsule drive and start over again with new backups
If you don't mind erasing the backup history on the Time Capsule and starting over again, this is of course the most economical way to continue. If you want to keep your old backups intact, then go with option 1 or 2.