I have often wondered this. If I attempt to download a large file, but get bored half way (let's say 50% downloaded) through and cancel the download, what happens to the 50% of the data that was "downloaded"?
I'm assuming you're talking about downloading a file from a website with a web browser here. Mainstream browsers like Firefox, IE, etc. store these files in a cache which will be cleared eventually. So, there is a chance parts of the canceled download remain on your computer in the browser cache, but they will be deleted eventually. If you wish you can force the browser to clear out the cache so nothing remains.
It depends on what you're using to download the file. A lot of software will leave the half-downloaded part sitting on your machine and may offer a feature where you can resume the download from the point you stopped it. The place where this file-part resides also varies depending on which software you're using. It could be in the place you chose to save the file, or it could be in a "temp" directory/folder. Sometimes the file-stub will be named a bit differently than the real file name ("myArchive.crdownload" instead of "myArchive.zip" for example) Other software deletes the file stub when you cancel.