And neither did Belle Zaringen, Diane Gotahel or Wanda Ringeise.

fpie...
To answer your question:

what does it mean to have a 25% greater chance of death without health insurance?

It means one or more of these are true:
1) you are talking about a different study from Health Insurance and Mortality in U.S. Adults conducted by researchers from the Cambridge Health Alliance and Harvard Medical School,
2) the person citing these statistics is making them up, or
3) the person citing these statistics has no idea how to deal with statistics.

The Harvard study (pdf file) is an excellent research product. The report, which is published in the current issue of the American Journal of Public Health is detailed, but quite readable.

In short, this study says nothing about specific individual risk. Rather, it discusses the impact of insurance on mortality across the U.S. population on an ANNUAL basis. (Although it looks at a population that was first identified and characterized in 1988, it is not a longitudinal study, so they cannot track whether the individuals gained or lost insurance coverage in the 20 years covered by the research. Therefore, it is a point-of-interview analysis, which means annualized data.

The researchers do discuss the application to individuals in the study limitations section and they also cite several studies that looked at this specific issue. Those citations are in the linked article, so you can look them up if you wish.

One thing that can be concluded: not having health insurance at any point during the ages 18-64 means your long-term health is more at risk. They also indicate that even for those who do have insurance, the out-of-pocket expenses have a negative impacts on mortality. Specifically, the Harvard researchers point out that other well-documented studies have found:
1) if you are uninsured at one point in the 18-64 age group, you are more likely to become uninsured again,
2) intermittent insurance coverage is common and accelerates the decline in health among middle-aged persons (ages 35-55),
3) among the near-elderly (ages 55-65), being uninsured at any point in time was associated with significant decline in overall health relative to those with private insurance,
4) regarding cost sharing (out-of-pocket expenses) among the insured, studies show that cost sharing worsened blood pressure control, and was associated with decreased use of essential medications and increased rates of emergency department use and adverse events, and
5) alternative measures of access to medical care for the uninsured, such as community health centers, do not provide the protection of private health insurance.

This is probably more than you wanted to know, but there is a lot more important information in the Harvard study than we are seeing reported. For example, the study notes a significant increase in the RATE of mortality in the past 20 years. They calculated the deaths among Americans aged 25 to 64 years associated with lack of health insurance and found that from 2000 to 2005 the number of people dying from lack of insurance increased by more than 140%.

Although they offer no speculation as to the reason for this horrendous increase (they controlled very tightly for more than a dozen variables) I suspect it could be due to the increased rate at which insurance companies are finding ways to deny coverage and dropping customers when they become sick. And, since that has increased dramatically since 2005, the obvious conclusion is that the actual number of people dying annually due to lack of insurance is probably greater than the 44789 deaths calculated for the 2005 data set.