The system in question is called the “Copyright Alert System” (CAS) and it’s described in full on this webpage. The system implementation has been delayed and is not likely to start on July 12th anymore.
The only real change that this indicates is that if you get copyright infringement notices from the RIAA or MPAA (those scary letters that they mail you when you are caught) the ISP will note that in their system and take progressively stronger measures, per letter received, to ensure that you are aware of what’s going on and that you stop doing it. The first four infringement letters that the ISP receives will just result in warnings, the fifth is a warning with an optional “Mitigation Measure” (slowed speed or temporary disconnect until you discuss the infringements with your ISP), the sixth is a mandatory “Mitigation Measure”. Permanent denial of internet service has NOT been agreed upon by the ISPs, disconnects will be temporary.
One last thing I want to be clear on: your ISP will not be actively attempting to catch you downloading illegally, they are only implementing a system by which, if you are caught by the MPAA or RIAA, you will be notified. This also means that legal torrents will still be fine: the MPAA and RIAA have no right to send infringement notices for content which they do not own, which means that your ISP cannot mark it down as infringement, which means that your account will not receive a notice or an alert. So basically, the ISPs have just agreed to be a little more cooperative with copyright holders and to keep track of when their customers have received infringement notices. If you receive a lot of infringement notices in the mail, then this could cause problems for you, but if your methods of acquiring content don’t usually result in infringement notices, this probably won’t really change much for you.