Neko atsume roughly translates to "cats collected" and this is an apt summary of the game. Players have a backyard typical of suburban Japan; by setting out food and cat toys, various (around twenty different) neighborhood cats come to do what cats do: play, sleep, and generally hang around. Players can take and collect photos of each cat in a notebook. Cats visit whether the player observes them or not, and they "pay" the player in sardines–the in-game currency–left behind when they leave (sardines can also be purchased with real money via microtransactions). Sardines are used to buy new foods and cat toys to attract more cats.
At this time the bulk of the game's text is Japanese with a peppering of English, but thanks to a tutorial and a graphics-heavy interface, it's easy to pick up and learn without any reading necessary.