This happens after Arya is attacked and stabbed by Waif but survives. Actress Lady Crane takes care of her and invites Arya to join their theater group. Arya refuses and Lady Crane asks her where will she go.
Arya: Essos is east and Westeros is west. But what's west of Westeros?
Lady Crane: I don't know.
Arya: Nobody does. It's where all the maps stop.
Lady Crane: The edge of the world, maybe.
Arya: I'd like to see that.
Basically, since we don't know anything from the show that Arya, or anyone for that matter, has any reason to suspect that there is anything west of Westeros, it is most likely that she just talks about going away and far, but likes the idea of venturing into unknown. Once she decides she is Arya Stark, she is going back to Westeros and to her list so this is forgotten. But in the moment of that conversation, she is nowhere safe, nobody is safe with her, she could run further east but west of Westeros is where nobody would look for her and it may sound exotic. There is no reason for her to actually tries to get a ship and crew and go on futile exploring journey simply leaving everything behined once she is confident enough not to run from faceless men.
From the books you can learn that Essos goes a lot further east, and is not unkown only it is too far away to consider. There are cities and populated areas... some members of various families are said to have gone in that direction, maybe even wild dragons may still exist. It goes on very far but there are contacts and informations about the lands there. South of Essos is huge landmass, much much bigger than known world and largely unexplored, full of wild tribes and fantastic creatures. There is no separate landmass to the north. although Westeros goes long way north covered in ice and snow (Land of Always Winter) and is unexplored even by the Ice-river clans or Thenns. It is huge frozen land and presumably where Others come from. There somewhere is where Night King's chased Night girls for thousands of years.
West of Westeros is just nothing, maps doesn't show. That should imply large body of water since it is unlikely that nobody tried sailing in that direction, just that there was nothing to map.
So if anything was implied with that line, it is a game of producers/writer, not of Arya as character. Arya would more likely just contemplate where could she possible hide from faceless men and it was witty to say.
If something might happen at that part of the world, it can be one of two things:
Some land mass is found by someone with something improtant like super high-tech flamethrowers and napalm bombs and aeroplanes that will help in fight against the dead. Or the Tolkien's Middle Earth. Or three-brested women that Littlefinger will kidnapp for new brothels. In other words, highly unlikely.
The Land of Always Winter actually is not exactly to the north of Wall and Westeros, but to the north-west and is not exactly clear how it goes further from there. So if that was a writer's hint, perhaps a group of heroes would have to travel far north and west to find some secret or to backstab the Night-King.