Normal and digital meters can only be read by physically visiting the property. Sometimes you don't have to physically look at Digital meters because they have a RF signal.
Smart meters transmit their power data through the power lines somewhat like ADSL over the phone lines. At the substation, they connect that to a normal network and can read your meter without visiting. In some cases smart meters work through the mobile phone network with GPRS or SMS messages.
Even smarter meters can download instructions from the power company to turn off AC or change the cost of your electricity at different times of day. This would replace the current ripple controllers that do similar things with more limitations.
Really cool meters have some sort of communications network within the house so the homeowner can purchase smart displays that talk to the meter and use it as a source of interesting information.