Recently Obama tried weasel out of his lie that "You can keep your plan, period." by claiming that he was helping the "Underinsured" by making them lose their crappy plans. Allegedly there are all these people in America that haven't bought enough insurance and he'll fix that by making them buy enough. Yes it's the standard paternalist claptrap, we know better because you're a five year old. However because these people can't actually imagine someone else's situation I'm going to give them a theoretical understanding of why.
To understand why underinsurance makes sense for a lot of people let's look at why people want insurance at all. People want insurance because the financial loss from a disaster causes more dissatisfaction per dollar than the financial losses from paying premiums. We know this is true because policy holders pay more on average than they receive in claims (absent idiotic government mandates to insure people at a loss). So they don't expect more money, yet they expect more value (otherwise they wouldn't do it) on average. So why would some dollars be more valuable than others? This is due to the "Law of Returns" that says the more you have of a resource the less valuable each additional unit of it is. Consequently the LESS you have the more valuable each unit of that thing is. In the event of a catastrophic event like your house burning down, a health problem that requires expensive surgery etc. you have lost things worth a lot of $, so you effectively lack a lot of $. Therefore each $ is worth more. While before that you have (relatively) a lot of $ so each one is worth less. Therefore it makes sense to sacrifice a lot of $ in premiums for a small average number of dollars in post-disaster dollars.
Consider the accompanying graph. Point A is your income without paying premiums. Point B is your income minus partial premiums and point C is your income paying full premiums that make good all losses in the event of whatever you're insuring against. Point D is where you are if you have a disaster and are only partly covered, "underinsured" in Obama's terms. Point E is where you are if you are totally uncovered in the event of a disaster. Notice how the majority of the benefit of being covered (the dark blue area under the curve from D to E) is provided by only partial insurance. The benefits from being fully as opposed to partly insured is the light blue area. Notice also that the pink area representing the additional cost of full premiums is larger than the red area of paying partial premiums. That's because what you give up to pay the extra premiums is more valuable than what you give up to pay the basic premiums. That's because you give up buying less valuable things first, that's how you know you consider them less valuable.
So say you insure your house and it would cost $100,000 to replace it it burnt down. Suppose also that you could afford to pay for $50,000 of the cost of rebuilding your house, either from savings or from making loans at reasonable rates. You no premiums and if your house burns down you have to spend money on rental accommodation until you scrape up the money. Maybe you even give up on owning a house and sell the land (maybe in a buyers market, since you don't know when your house will burn down). Or you could pay for a $100,000 policy and if your house burns down the cost is minimal (other than the sentimental value of heirlooms etc). I'm assuming here everyone gets out safely BTW. Or you could get a $50,000 policy and if your house burns down you can rebuild, but you have to work overtime to pay off the loan, the holidays for the next few years are at your sister's place etc. The middle course obviously avoids the majority of the harm of a fire, while only costing half the cost of full insurance. That doesn't mean that everyone is better off underinsuring, it depends on how you value the various outcomes. It does mean that it is possible to want insurance and not full insurance, so "under-insurance" can make sense for some people.
Of course there is additionally the fact that people who underinsure are sometimes lower risks on average. For instance if you know that you are unlikely to have a car crash (because you don't drive much) you might be more likely to underinsure. If this is true in a market then under-insurers might get a better deal from insurance firms who know the risk of insuring them is lower.
However whenever I've heard of "under-insurance" on the news it's always presented as a bad thing, whether by the Obama team who criticize other's healthcare choices or in bushfire season, where fire insurance executives will often warn of under-insurance. Don't listen to them. If you want to under-insure, do it.