Memories!
A memory box is just any variety of nice box (cigar, shoe, bread) that is filled with trinkets and knickknacks that remind you of better days. You can decorate them with any manner of artistic or memory-infused collage and in no time, you're collecting memories!
My memory box has lots of good stuff in it:
One ancient cork-postcard from Italy with a crusty old man on it.
Three cicada shells in various poses.
Three golden leaves.
One rusty letter opener.
One coiled length of branch.
Two seashells.
One cut of German flag cloth.
One Navy diver belt buckle.
A few dozen miscellaneous tickets from events, collected in a thin yellowed envelope.
Your wife's head.
I won't tell you what the items memorialize, because it's always more fun to guess!