In Ark: Survival Evolved, the concept of Game Persistence applies. This means that on the player servers, the in-game world always changes, even if there are no players online.
Your character, everything you built, and your Pets, stay in-game even when you leave. While the food and water consumption of all player characters freezes when they log off, the food and water consumption of tamed dinosaurs does not, which means they can starve while you're offline.
You can physically move your character and items between the network of ARK's by accessing the Obelisks and uploading (or downloading) your data to the cross-ark. This means there exists a cluster of ARKs, each slightly different than the previous, which are always online and change persistently.