An exploit virus is a widely spread term within the community working with computer security to denote the software which uses any kinds of bugs, holes or vulnerable pieces of code. This usually results in the privilege escalation or the process, often referred to as denial of service. All this happens to your operating system regrettably.
Several methods are used to classify exploits. The most common one uses the way the exploit virus connects with the vulnerable software to classify things of a kind. A remote exploit virus operates with the help of the network thus not gaining any access to the vulnerable system until it uses the security vulnerability of this system. There is also a local exploit virus, which usually tries to get prior access to the system under vulnerability and as a rule widens the rights of the creator of the exploit virus to an extent which is granted to the system administrator only. There are also exploits against the client-side applications, they usually consist of the specially modified servers that use an exploit virus if the server is contacted by the client application. Sometimes these exploits need some consent or agreement from the user (interaction is required) thus they are used along with the methods of social engineering (social engineering is something connected with psychology, when one does another person do something they wish with the help of the activity beyond that person's understanding).
Another method to classify exploits is through the type of the vulnerabilities they usually attack. These include buffer overflow, format string attacks, race condition, cross-site scripting, integer overflow, SQL injection, cross-site request forgery etc. vulnerabilities.
Sometimes exploit viruses are divided to such varieties as unauthorized data access, dos exploit, dso exploit virus, code execution etc., which means they are classified by the action done against the vulnerable system.
Often the exploit virus is specially designed to allow its developer gain a root-level access to the vulnerable computer system. It is however possible to use several different exploits to gain a low-level access at the beginning and then use different exploit virus to widen the privileges quite to the root-level.
Usually a separate exploit virus can only explore one specific vulnerability of the software under attack. Very often, after the exploit virus code has been published, the developers of the vulnerable software fix their bugs and this very exploit can no longer cause harm through using these vulnerabilities. That is why some hackers who invent the most dangerous exploit viruses often avoid publishing their exploits, but try to keep them in secret only to themselves or other hackers of the same team. This kind of exploits is often referred to as the "zero day exploits" and other inexperienced hackers (script kiddies) dream of obtaining access to such an exploit virus.
Ordinary user can not protect themselves against all these horrible exploits. The most popular methods to combats viruses like "never open suspicious or unknown applications, never download or run them" etc. will never help against the exploit virus.
Exploits use vulnerabilities of the software you use and the responsibility lies on the developers of this software. The only thing is to hope for the best and that the developers would fix all their bugs until the exploit uses them to attack your computer.