It depends on the firm, but Apple is a great example of a company that took out tons of debt to buy back shares (and pay dividends) and it made total sense. The reason was they were holding tons of profits from overseas that they didn't want to pay tax on. Apple being Apple was able to get really low rates on bonds and that turns out to be way cheaper than paying tax and using those profits for anything.

Interest rates are moving up now, but have been really low for a long time. If you pay out a decent dividend it can make financial sense to loan money to buy back shares just on not having to pay the dividend (if you pay a 5% dividend like Ford does, but can issue bonds at 3%, I mean why not?).

There's also the factor that since interest payments are tax deductible, it further pushes the cost of interest rates lower.

tl;dr it usually comes down to tax and accounting reasons.