Taxable Spinoff
  
See: Tax-Free Spinoff.
You run a novelty underwear company. You want to get rid of your glow-in-the-dark thong division. You're going to spin it off as its own company.
There are a couple of ways to structure the deal. Some result in capital gains taxes for the parent company. These fall into the "taxable spin-off" category. These happen when the company is sold to an outside party (say, a hedge fund comes in and buys the Bright Thong unit to set it up as its own company). Also, conducting an IPO for the new company could result in taxes for the parent company.
However, you do have choices that avoid the taxes. You can conduct the spin-off in a way that would be tax-free. For instance, you could issue shares of the new Bright Thong's stand-alone company to your shareholders. They would own both the parent company and the new company, in equal proportion.
The tax-free option obviously has the appeal of avoiding taxes. But it doesn't bring in any cash for the parent company. It just serves to separate the businesses. The taxable model can be useful if the goal of the transaction is to raise capital for the parent company.