I was an Edwards supporter during the primary, but I'll try to include some of the opposition's frequent critiques in this description.  Remember, though, that "unbiased" descriptions don't really exist.  Trying to describe someone as perfectly neutral is just as biased an approach as trying to describe someone as good or bad.  Like, if the facts show that someone is clearly awesome, spending as much time on their faults as you do on their achievements is a biased way to write.  

You can get a brief bio on the old Edwards campaign site.

Edwards is a wealthy man right now, thanks to his success as a trial lawyer.  His opponents occasionally argue that his wealth distances him from the common people he claims to represent, and makes it difficult for him to be an advocate for their interests.  He claims that he grew up knowing the difficulties faced by the working class, so he knows the people he fights for.  He also argues that his success was made possible by Roosevelt-era policies that provided for good public schools, tuition assistance, and a strong social safety net.  He says he wants to protect these programs so that Americans can continue to live in a country "where everything is possible."  Additionally, he earned his wealth by working very successfully to represent the interests of common people whose lives had been disrupted by the decisions of the powerful.

Some doctors (not most) claim that he was an "ambulance chaser" who represented patients in unreasonable lawsuits that preyed on doctors and drove healthcare costs up.  It is true that some of the medical science that he used as evidence in these cases has been discredited today.  But at the time of the suits, the science was state-of-the-art.  The hospitals and doctors he opposed in court had made decisions which the majority of the medical community at the time considered shameful and inept, and those decisions had lead to severe disabilities which would afflict the plaintiffs for the rest of their lives.  According to the best wisdom of the time, the lawsuits were anything but frivolous.

Before he began his run for the Senate, Edwards knew that people would call his lawsuits frivolous, so he hired an independent team of lawyers to go over his entire case history.  They could not find one lawsuit that could be called frivolous, by any legal standard.  

Non-medical cases that Edwards tried and won included a lawsuit against a trucking company that encouraged its drivers to drive long hours at high speeds.  An overtired employee of that company had struck and killed both of the parents of the boy he was representing.  After the suit, trucking companies across the US moderated their policies to encourage their employees to drive more safely.  

In another suit, Edwards won a large settlement from a company that made drain covers for wading pools, on behalf of a young girl whose intestines had been sucked into a pool drain because of the faulty cover.  The company had known about the safety problem, and internal documents showed that they knew of eleven other children who had been wounded and disabled in the same fashion by their pool drain covers.  They could have corrected the problem in their product with the addition of a cheap screw.

Edwards argues that court victories like these not only improve the lives of plaintiffs who have been life-alteringly harmed.  They also improve public safety by making corporations consider it in their bottom line.  Opponents argue that large rewards like these are inequitable and damaging to the economy.  They claim these rewards create an overwhelming timidity about litigation in the corporate world, inhibiting progress.

Edwards and Kerry now share the same campaign platform, which can be perused at Kerry's web site.  Some issues that Edwards says are especially close to his heart, though, are the elimination of poverty in America, the wealthiest nation in the world, putting limits on the power of Washington lobbyists, encouraging American companies to employ Americans, and regaining the worldwide respect that America once enjoyed.