Unsystematic risk is the risk you take on when investing in a stock. Basically it is the risk of some new announcements, or earnings reports coming out that could affect the price of the stock.
So if you buy a stock thinking it was a good buy and all of a sudden the company comes out with earnings that are far below expectation the stock might react harshly causing you to lose money because of some unforeseen events.
However there are ways in which you can prevent yourself, or lessen your chances of taking unforeseen losses.
If you are an investor and are holding for the long term one thing you can do is to buy many different companies. If you only have 1 stock and some bad news comes out about that stock it will drastically affect your portfolio.
However if you have 20-30 different stocks and some bad earnings comes out for one of your stocks it will not affect your overall portfolio as much. In fact if your other stocks go up far enough you might actually make money when one of your stocks has a big surprise.
If you are trading stocks there is still the risk of the unforeseen happening. So you should still be prepared for it by using things like stop losses and risk management.
Another great idea to limit your unexpected risks when trading, is to simply not be in a stock that is about to give off an earnings announcements. These announcements come out every 3 months or so and can really move the price of the stock (in either direction).
So it can be a good idea to avoid being in during these times. There will always be positions out there that you can take without having to worry about earnings.