What does it mean to roll over debt?

It's similar to refinancing but generally has a slightly different connotation.

If you have an existing loan that has a balloon payment and you take out a new loan to pay off the old loan, that would be rolling over debt. That's something that is extremely common for companies that issue fixed term bonds-- if Bob's Widgets issues 5 year bonds today, it is very likely that they will roll that debt over to a new bond issue in 5 more years. It is generally less likely for individuals since most consumer loans are fully amortized (you make payments every month until it is paid off) rather than a balloon payment at the end although some people do have mortgages with balloon payments or things like payday loans where the entire loan is due in a single balloon payment.

If you have an existing loan that you could continue to make monthly payments on and you decide to take out a new loan because the new terms are more advantageous, that would generally be called refinancing.

Now, that being said, there are plenty of corner cases where you could use either term. If a company issues new bonds in order to redeem some callable bonds that aren't due for several years, that could well be called a refinance even though it would probably be called rolling over the debt. But these are corner cases, most of the time it is relatively clear.

In general, rolling over debt is a riskier thing than refinancing because rolling over debt is generally something that the debtor has to do at a point in time, not something they can choose to do whenever it benefits them. If a company happens to have a bad quarter just before they need to roll over a bunch of debt or a consumer has to roll over their mortgage just after they lose their job, that generally creates a lot of issues and means that the rate on the new debt is going to be much higher than the old debt. If you're refinancing, that's something that you can easily choose not to do if you find that it's going to be more expensive.