If you're interested in seeing what's happening, fire up Activity Monitor and hit Sample on the app when you see the beach ball. It records the call frames of all threads a couple of thousand times over a few seconds, so you can see what that app is waiting for.

... and report the bug to the app's developer! Be sure to include the sample.

If the entire system has ground to a halt such that it's difficult to actually get to Activity Monitor to do the sample, then it's likely to be a memory problem. If it's just one app, it's probably something else.

If the system is hung such that you can't get Activity Monitor to sample, use command-option-control-shift-period to run sysdiagnose. Attach the resulting /var/tmp/sysdiagnose_$(TIME).tar.gz to your bug report.

And inside that tar.gz file is a spindump.txt file, which will have the samples of whatever application is spinning at the moment, just like if you used Activity Monitor to sample it.

I had never heard about it... Wonderful.

good idea - upvoted! :)