1. To perform any repetitive or monotonous thought exercise as a means of calming the mind to try to fall asleep (such as the traditional sleep aid of counting imaginary sheep). Whenever I go to bed with a racing mind, I make myself count sheep until I drift off to sleep.

2. By extension, to be kept awake at night or experience insomnia. Usually used in the continuous form. After I lost my job, I was up counting sheep all night, trying to figure out how I'd make ends meet.