As an example, if you instruct your antivirus software to delete all infected files, those that were infected by a true file infecting virus could also be deleted. This could impact the normal features and functionality of your operating system or programs you use. On the other hand, antivirus software can't 'clean' a worm or a trojan, because there is nothing to clean - the entire file IS the worm or trojan. Quarantine plays a nice middle ground, because it moves the file to safe storage under control of the antivirus program - so it can't harm your system - but it's there in case a mistake was made and you need to restore that file.
Clean: attempts to remove the infection from the file. This is only pertinent to virus behavior, wherein a legitimate file has been 'infected' with non-legitimate (usually viral) code. Quarantine: attempts to move the file to a safe location that is managed by the antivirus software. Delete: Removes the file completely from the system.
Generally speaking, if it's a worm or trojan then the best option is to quarantine or delete. If it's a true virus, the best option is to clean. However, this assumes you are actually able to distinguish exactly what type it is - which may not always be the case. The best rule of thumb is to proceed from safest (from a recovery standpoint) to least safest (files are gone forever).
Start with the 'clean' option. If the antivirus scanner reports that it cannot clean the file, then choose 'quarantine'. Only choose 'delete' if (a) the antivirus scanner specifically recommends it*, or (b) you're absolute certain that it's not a legitimate file, or (c) there's just no other option.
*It's worthwhile to check the settings in your antivirus software to see what options have been preconfigured and adjust accordingly.