Normally, I'd say the process stopped or something and just revert from a previous save, but this error is a little different. The cursor isn't frozen and sound is still playing. The interface responds to a point, but it refuses to advance.
There are still sound responses when I try to interact with the interface (beeps when I click to reload) and tooltips still appear when I hover over an icon. Camera rotation still works as well. However, gameplay does not advance and it's stuck on my last soldier's turn.
This is also not a one-time occurence, I have encountered this error in the past. However, I'm not sure how to reproduce it, although based on the last event, it happened when I uncovered an enemy on my turn.
NOTE (2013/03/22 5:14 CST): Happened again, although this time was with trying to get a soldier into Overwatch.
Best Answer
This is a known (I hope!) bug at the time of writing. There's not much to do currently except wait for a patch. The bug is rare and seems to strike me randomly, and I have not been able to reproduce the error. The few times it's happened I've been forced to kill the process and load a save-game.