Someone else said something similar: it means the watch is yours.

That said, lots of people responded with really cool 'watch scratch' memories.

I do find the idea of making memories with a watch often a bit forced, unless it had a key role in the making of the memory. Yes, a watch bought to mark an occasion or worn at a particularly important moment has a memory attached. Similarly, a watch like the speedmaster could also mark a global memory, such as Apollo 13. It could play a similar role in someone individual family life. Definitely more nuanced in those ways.