To transfer data or (especially) code from one computer to another. The distinction between downloading and uploading is hazy but downloading often refers to transfer from a larger "host" system (especially a server or mainframe) to a smaller "client" system, especially a microcomputer or specialised peripheral.
However, note that ground-to-space communications has its own usage rule for this term. Space-to-earth transmission is always "down" and the reverse "up" regardless of the relative size of the computers involved. So far the in-space machines have invariably been smaller; thus the upload/download distinction has been reversed from its usual sense.