Tar (for "Tape ARchive") is a UNIX shell command that creates a single file called an "archive" from a number of specified files or extracts the files from such an archive. A tar archive has the file suffix ".tar". The files in a tar archive are not compressed, just gathered together in one file.
The name is derived from a time when files were commonly backed up on and occasionally retrieved from magnetic tape as a permanent storage device. (They still are in some data centers.) A tar archive is perhaps more frequently used today to transfer files among UNIX systems. A popular archive handler for Windows systems, WinZIP, can be used to extract the files from a tar archive.
Tarball is a jargon term for a tar archive, suggesting "a bunch of files stuck together in a ball of tar."