What is the icon on the desktop after I install an application?
This is the downloaded disk image. Many applications downloaded from the internet will come as an internet ready disk image, which means that it mounts and opens when the downloaded file is opened.

A disk image is a mountable image of any volume. Disk images can be images of physical volumes or virtual disks. Like a zip, dmg disk images can be compressed (and usuall are, especially internet ready disk images such as the disk images used to install software from the internet) or can be read/write like an actual disk. They are mounted in the same mount point as physical disks, but are virtual. When unmounting, the disk is ejected and the mount point deleted like a physical disk. As the disk image is a disk, it will be shown on the desktop if you have the relevant option selected in Finder preferences:



Copy the app to your /Applications folder (or wherever else you desire) then eject the disk image by right-clicking and selecting Eject (or through Finder). The mounted disk image is the .dmg that you downloaded, therefore can be deleted by deleting this disk image after unmounting.