Cat staring at nothing
A cat staring at nothing is most likely watching a spot where something moved (a fly, a shadow, a sound in the wall) and may keep watching it long after the thing is gone. Cats hear far higher sounds than people do.
What it may mean
Cats are loyal to the last place they saw something. In experiments with hidden toys, cats search right where an object vanished, and at home the same habit looks like a vigil: a cat fixed on the gap behind the fridge an hour after a moth went in, or on a bare patch of wall where a reflection once danced. To you the corner is empty. To the cat it is the place where something happened. People keep vigils like that too. They check the phone for a message from someone who stopped writing months ago, drive past an old house, wait at a spot where a chance once appeared. Some of that watching is patience and some of it is habit that outlived its reason. A cat on watch keeps that kind of loyalty without asking whether anything will come back out of the gap.
Depending on how you saw it
Fixed on the ceiling
Up near the ceiling there may be a tiny spider, a fly or a patch of light thrown by a phone screen or a watch face, all easy for a cat to see and for you to miss. Which tiny movement in your day steals more of your attention than it deserves?
The same corner every night
A cat that watches one wall or one cupboard night after night may be hearing mice, insects or pipes ticking as the house cools, sounds pitched too high or too faint for people. What does your home do at night that only the cat seems to know about?
Why it happens in nature
Cats hear sounds far higher than people can, well into the ultrasonic range where mice and insects call, and they are very sensitive to small movements and flickers of light. In experiments, cats looking for a hidden toy tend to search where they last saw it disappear, so a cat may keep watching a spot after whatever moved there has gone.
To reflect on
What spot in your life are you still watching after the thing that moved there has long gone?