There are a variety of terms depending on what you're doing. In order of their chances of successful recovery these are:
1. Move to trash
You just move the file into a generic "recycle bin". You can fish it out later if you need to. Not secure at all. Perhaps this would be "security by obscurity" if you didn't know where the trashcan was.
This is usually synonymous with moving a file into a "marked for overwrite" state. The underlying operating system sets a flag against the file stating that it's OK to use the space occupied by this file. This overwrite may occur as a result of a system defrag operation, or maybe disk space is getting a bit tight. Often you can easily recover this type of operation using free online undelete tools.
3. Secure delete, wipe, shred
This involves marking the file as in the "delete" operation. In addition, a process immediately overwrites the data using a random set of data. Some implementations overwrite the data many times in many different ways to ensure that it cannot be recovered by conventional tools. Depending on the strength of randomness and the manner in which the write process interacts with the underlying medium (e.g. is it magnetic tape, magnetic disk, flash memory etc) it is possible to still retrieve data through forensic techniques. Perhaps using a super-conducting quantum interference device (SQUID) or somesuch.
4. Forensic delete
The final word in data destruction. All trace of the data is completely removed from the medium in a manner that renders it utterly impossible for it to be reconstructed through forensic techniques. This is normally physical destruction or putting the medium of data storage out of reach (dissolved in acid, buried in a nuclear reactor, blasted into space etc).
Hope it helps.
Undeleted my own answer in response to @Developer Art's comment. Somewhat apt given the context of the question, eh?