A sick-out is a way of going on strike without calling it a strike: on the same day, all the workers at a company phone in and say they are sick, and then stay home. Everybody knows they are not really sick. That is the point — the message is clear, but nobody has officially refused to work, so it is much harder for the company to punish anyone. You will hear it most about workers who are not allowed to strike by law, or who would lose too much by striking openly: air traffic controllers, police officers, bus drivers, teachers, nurses. It is an American word, quite informal, and it belongs mostly to news reports and workplace talk rather than to books. You write it with a hyphen; some newspapers write sickout. The verb phrase behind it is "call in sick" (to phone your workplace and say you are ill), and a sick-out is that, done by everyone at once, on purpose. Because it is a countable noun you can say a sick-out, two sick-outs, stage/hold a sick-out.