The save function is commonly represented by an image of a floppy disk. The use of this icon derives from 1970's to 1990's, when files were typically saved on floppy disks. For younger users the use of this icon might seem quite arbitrary. It is recognizable mainly since it's been so widely adopted.
Originally the floppy disk icon was only used as a reference to a disk that was inserted in a computer, but later on it became the standard icon for saving files. In Microsoft Office the floppy disk icon was at least used in version 2.0 ( 1991), but earlier occurences are likely to exist.
MS Office 2.0 1991.