Waiting for a drink maybe? My cat won't touch water in a bowl, but follows me into the bathroom, jumps in the sink and looks at me until I turn the tap on to a slow trickle so she can have a drink.
Cats do the strangest things! One of ours sits and stares at the kitchen bin! He did catch a bird once which went behind there but I rescued it and let it go. I think he thinks it's still there!
For the joy of watching you fret. One of mine jumps in the basin most nights and licks round the plug as though she's desperate for water - when there's a perfectly good bowl of the stuff downstairs.
Cats seem to prefer to drink water above ground level, this makes sense as it would be more likely to be unpolluted rain water in the wild. Cats also are programmed to watch anything that moves and have a good memory for where things have been seen to move. Our cat used to love chasing the red spot made by a laser pointer and every time we had this game I made it appear to emerge from under the sideboard and disappear there when the game was finished. When he was bored he would sit in front of the sideboard waiting for it to come out to play.
Some cats just love licking water from the tap and wait there for it to run. However, how old is the cat? We had an 18 year old cat once who went senile and would spend hours just sitting in places staring at things, including her food bowl - full or empty, made no difference.