This is about whether a person should start a savings account for "life happens" fund or put every penny toward paying off debt. Ms. Singletary (and I) both recommend trying to do both, even if your savings amount is small.
The reason for doing this is that "life happens" to ALL of us, without exception. Something is always going to come up that you didn't expect. If you are putting ALL of your money toward paying off debt and have no savings at all, then when some small emergency comes up, you end up having to charge it AGAIN, thus wiping out some of the progress you've made, and adding to your overall interest charges.
If you can build up even a small "life happens" fund, say $500 or so, then you've got some fall-back money. That would be enough to pay for, say, a small car repair, or a new tire if you have a blow-out, or a dental emergency if you chip your tooth, for example.
The point is to have a little buffer between yourself and having to use your charge card again and again when it could be avoided.