When you log on to the internet, your internet service provider assigns your connection a number that is used to identify you. This number accompanies you throughout your surfing expedition and can be used to identify you in the event you engage in any illegal or malicious activity. This, unless you are engaged in anything illegal, is not worth concerning yourself with. Your internet provider does keep track of your internet surfing habits, but does not do so in order to report your habits unless it is legally required that it do so. This fact is what concerns the hacker.
Hackers are probably more aware of security measures than are the average surfer.
The reason for this is that they fear discovery, detainment and prosecution. One method they can use to allay suspicion away from them is to impersonate some poor unsuspecting soul. What this means to you is if your IP is hijacked, every activity that is performed by the hacker using your IP will lead back to you. This can prove to be an inconvenience at least, should that hacker break into a site and pilfer through and use stolen credit card numbers, or engage in some such other illegal activity. It will eventually be proven that you are innocent, but in the mean time you will have to worry about lawyer bills, posting a bail bond and having your PC studied forensically for quite a while.