Acronym for Random Access Memory.
32MB of memory can be a reasonably useful Linux install if you don't have X(1) or any other memory hungry programs running. 32MB of memory would make a reasonable non-caching firewall for instance.
128MB is a reasonable amount of memory for a Linux install, but if you want to run Mozilla, and other memory hungry programs you probably need:
256MB or 512MB. 512MB is a nice amount of memory. I have 512MB on my desktop, which is also a fileserver.
1GB of memory is just getting silly :)