Question: What are Flash exploits? Will they damage my computer? Should I not use Flash?
Answer: A Flash exploit is a security vulnerability that takes advantage of "backdoors" in the code that executes downloaded Flash movies on your computer in order to inject and execute malicious third-party code that could be anything from a keylogger to a data miner to a virus. This can not only damage your computer but your personal life, should information be gathered that gives access to your finances or personal information - which can lead to identity theft.
Does this mean you shouldn't use Flash at all? No. It does mean that you should always keep your version of Flash up to date, and always be careful in your browsing habits - something you should be doing anyway. Browse with common sense, make sure your browser's security and trusted site settings allow you to have absolute control over what is and isn't viewed on your computer, and if necessary, use plugins like NoFlash (Internet Explorer) or NoScript (Firefox) to block all Flash content unless you specifically allow it to play.