The VIC-20 had connectors for game cartridges and a tape drive (compatible with a C64). It came with five kilobytes of RAM, but 1.5 KB were used by the system for various things, like the video display (which had an unusual 22x20 char/line screen layout), and other dynamic aspects of the operating system (such as it was). The RAM was expandable with a plug-in cartridge which used the same expansion port as games. Port expander boxes were available to allow more than one cartridge to be connected at a time.
RAM cartridges were available in several sizes: 3K, 8K, 16K and 32K. The internal memory map was re-organised with the addition of each size cartridge, leading to the situation that some programs would only work if the right amount of memory was available. The 32K cartridges were all third-party and had switches to allow the RAM to be enabled in sections so that any expansion size could be achieved.
BASIC programs could use at most 24 KB of RAM. Any extra occupied the location usually used by ROM cartridges (i.e. games). This allowed people to copy ROM cartridges to tape and distribute them to their friends, who could load the tape into the top 8k of their 32k RAM packs.
The name "VIC" came from the Video Interface Chip that was also used in the other, later, Commodore 8-bit computers.