Traditionally, a virus payload referred to action a virus might take beyond simply infecting files. This payload could range from the virus displaying a dialog box with the words "Have a Good Day" to a virus that overwrites or deletes files on the system. For example, the circa 1998 CIH virus had a payload to overwrite the Flash BIOS of systems, rendering those systems unbootable. LoveLetter also deployed a malicious payload as part of its routine, overwriting certain media file types.
Today's malware is less likely to include a payload that damages files on the system, but instead typically include a payload that allows backdoor access to the system and steals passwords and other sensitive data.