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To transfer data or programs from a server or host computer to one's own computer or digital device. Compare upload.
To transfer data from one computer to another. Downloading usually refers to transfer from a larger "host" system (especially a server or mainframe) to a smaller "client" system, especially a microcomputer or specialised peripheral, and "upload" usually means from small to large.
Others hold that, technically, download means "receive" and upload means "send", irrespective of the size of the systems involved.
Note that in communications between ground and space, space-to-earth transmission is always "down" and the reverse "up", regardless of size. So far the in-space machines have invariably been smaller; thus the upload/download distinction has been reversed from its usual sense.