If you don't check while you are still at the store, you will find that many plants you bring home will be rootbound. Before you buy a plant, if you turn it over and if roots are shooting out of the drainage hole, chances are that the plant is rootbound or sometimes called potbound. Once you take the plant out of its nursery pot, if the plant is rootbound you can see that the roots have completely taken up the pot, often circling and creating a dense web of roots. This can form a compacted, hard ball that comes out of the pot with effort, retaining the shape of the pot.
This means the plant has been in its pot for too long and that potentially it has not been getting the nutrition it needs from the soil because there simply isn't enough potting soil left in the pot because it has been replaced with roots. It also may mean the plant is stressed from lack of nutrition and drying out again and again.
The other problem with a rootbound plant is that if you don't separate the roots and plant it as is, the roots will continue to grow in the same circular pattern as in the pot, not spreading out to take advantage of soil and water, eventually even strangling the plant.
Depending on the plant, it's relatively easy to fix the problem, but it may take some strength and courage because you will have to rip or cut the roots. What's important to remember is that most plants are pretty tough. Though some don't like you messing with their roots, most will be just fine and will grow better after their constricted roots have been untangled or cut.
The goal is to allow the plant to spread its roots so what I do with a rootbound plant is first to try to peel the roots away from the ball they have formed. For some plants, like pansies or annuals, you can usually just tear the compacted roots with your hands. I tear off the bottom and then rip up the sides. Sounds brutal, but it works.
For plants with bigger tougher roots, I take a serrated knife or sharp shovel and cut the roots, either making slices down the sides of the plant or making a cross cut on the bottom of the plant, then spreading out the four quarters of football I'm left with.
While it's better to try to buy a plant that is not rootbound, I find that sometimes there is no choice. Almost all moms, and many spring flowers--pansies, violas and many hanging baskets are totally rootbound. The good news is that I have rarely (if ever) killed a plant from the treatment described above.
For more info on dealing with rootbound plants
Also Known As pot pound, root-bound, root bound