The Business Insider has a great post mortem on what exactly Barbour's demur means.

Now that he's out, the GOP race hinges on whether former Arkansas Gov. Mike Huckabee decides to get in. His former campaign chairman, Ed Rollins, says that he will. If he does, he seems a prohibitive favorite to win the Iowa caucuses, a likely loser in the New Hampshire primary (to Mitt Romney), thus setting up a showdown between the Christian and the Mormon in South Carolina. Huckabee wins that in a walk and probably sweeps the remaining Southern primaries and becomes, de facto, the GOP nominee. Republican presidential candidates who carry the South in the primaries win the GOP nomination.

Last cycle Huckabee won Iowa in a major upset of Mitt Romney, avoided NH and nearly beat eventual nominee John McCain in the South Carolina primary. And he did all that with a bare-bones political operation put together long after other candidates had state-level operations set up across the country.

Lately he has been leading in a wide array of national and state level polls, performing best against Obama in a number of key battleground states. While he's avoided outright politicking, he has also had his own show on Fox News, which is pretty much the biggest Republican primary audience available. 

Not everyone thinks Huckabee will get in though. Ed Rollins may think he's going to run, but a number of his top Iowa operatives have already been hired away by other candidates. Some have speculated Huckabee likes making big money in the private sector, most recently building a $3 million home in Florida, and will avoid a Presidential run where he would have no income for the next 18 months. 

With candidates that everyone thought were sure bets to run, like Barbour or even John Thune, deciding not to run, it can't be expected that Huckabee will throw his hat in. But Barbour begging off just made Huckabee's prospects a whole lot brighter.