The rationale is that Congress decided people ought to have access to care for their health problems (there are efficiency arguments against having a health system with a large uninsured population but the visceral argument is the simplest and most direct). But if that's the case, insurance markets--particularly the ones in which people who don't have group insurance plans through their jobs have to shop-- have to work differently than they have in the past. And part of that means there has to be something in place to eliminate or at least blunt the bad incentives that would otherwise be created for people to just free ride until they get sick. That's what the individual mandate is for. It's the price we pay for having a private system that also aspires to give everyone, no matter how sick, access to care.
As for whether people will generally pay the fine or not, that remains to be seen. In Massachusetts, most people have opted to get something for their dollar. Ultimately it's the choice between paying less and getting nothing or paying more and getting something.
Insurers won't be able to turn you away but that doesn't mean you can buy insurance in the ambulance and everything will be fine for you. There's going to be a seven week open enrollment period each year (October 15 - December 7) in which you can enroll in a new insurance plan in the new marketplaces; except for in certain special circumstances, if you don't buy during that window you can't buy it in those marketplaces. Meaning if you go uninsured and have a heart attack in February, you can rack up quite a few bills that are solely your responsibility before you buy a health plan during open enrollment in the fall.