Memory and Memories are two different things.
The Memories you are talking about came with Generations, they're things like
Christopher Steel just caught a 20kg fish! or
Agnes Crumplebottom just WooHoo'd for the first time. The Memory the game is talking about is what is called "System Memory" - which is something completely different. I'm not a hardware expert, so I can't explain what it is in any great depth, though, so here's a (very) simple analogy:
Your PC is a storage cabinet. You doing stuff is putting information into the cabinet. Your cabinet isn't infinitely large, it stops somewhere, and eventually you're going to hit it unless you remove stuff. When you use Word, Chrome, whatever, you don't use an awful lot of memory, so stuff goes in slowly and can be removed quickly (ie Word takes a few seconds to close). Sims, however, is a bit worse in this department. So you're pouring stuff into the cabinet, and not removing it quickly (ie, for me at least, Sims can take upwards of 5 minutes to close). You can see where this is going. Eventually, you try to cram something into the cabinet, but it can't fit - it's
out of memory. So when you try to save, a message pops up telling you it can't.
Moral of the Analogy? Save lots, save often on a lower end PC. On a higher end PC, you don't have to save as much, but still should.