It's the Domestic Issues, Stupid
There's lots of talk about Edwards' charismatic appeal, but John Nichols at The Nation sums up perhaps the biggest plus to his place on the ticket:

Above all, however, Edwards brings to the Kerry campaign something that has been missing to this point: a recognizable and appealing domestic-policy message. Kerry secured the nomination by playing on his record as a veteran and his foreign policy and national security experience. Democratic caucus and primary voters bet, perhaps wisely, that those strengths would be needed in a race with Bush. But Kerry never developed a functional, let alone inspiring message for the home front. With his talk about the need to close the economic gap between what he referred to as the "two Americas," and with his emphasis on developing programs to aid the working poor, Edwards renewed old Democratic Party themes that will play very well--especially with wavering Democrats and independents--in a year when pessimism about the economy could yet decide the direction of the presidential race.