When you download a file in Apple's Safari Web browser, the file will be listed in the program's Downloads window, which can be accessed by either clicking the small down-arrow toolbar button or using the Option-Command-L keyboard shortcut. This window will show a history of all recently downloaded files and those in progress, but has a few more organizational functions than simply being a basic list.
First of all, you can remove files from the list. To remove all entries, click the Clear button; you can also remove files individually by right-clicking them and choosing "Remove from List." Files can also be removed in batches by selecting multiple files using the Shift key or Command key and pressing the Delete key at the same time.
The Downloads window can also be used as a launching point for the files it contains. Each entry in the window has a small spyglass icon that can be used to reveal the file in the Finder, but you can also open the listed file directly by double-clicking it to launch its default handling program.
You can also use the Downloads window to move your downloaded files. While you may be accustomed to opening the Downloads folder (either directly or by clicking the spyglass) and moving the files to another location in the Finder, you can instead drag individual files or group selections from the Downloads window to a location of your choice, such as Finder folder or the Dock. You can also use this to open them in applications besides their default ones by dragging them to the application icon of your choosing.
The last detail about Safari's Downloads window is that it will not work if you enable Safari's private browsing feature. In this mode, even though the downloads in progress will appear in the Downloads window, once finished they will be instantly removed. Unfortunately during the download Safari encapsulates the downloaded file in a ".download" container, so clicking the spyglass to reveal it will only work while the file is being downloaded, and once the download is completed the file you revealed will disappear.