The term "bare root", when used in gardening, refers to a plant that is offered for sale with its roots exposed rather than planted in soil. This is a fairly common way for some plants to be sold when they are being shipped a substantial distance, such as when you order them from a mail-order retailer.
Not all types of plants can handle being shipped this way. However, for those that can, such as roses, fruit trees and shrubs and several perennials, including hosta and daylilies, it is perfectly acceptable.
Perennials and roses may also be sold as bare roots on the shelves of some of your local retailers. Big box home improvement centers and mass merchant retailers will often sell these plants as bagged or boxed bare roots. This is a perfectly acceptable way to buy plants, though you should inspect the roots through the plastic bag to make sure they firm and not soft or desiccated.
Plants sold bare root are dormant when they are shipped, and should be planted ASAP. Better mail-order retailers will understand this, and won't ship your plants until the time is right for planting in your region. If it is impossible to plant them immediately, then keep your plants chilled but not frozen until you can plant them. Normally, bare root plants will arrive with the roots bound together and the root ball contained in plastic, sometimes with a bit of peat moss or sawdust to absorb excess moisture and prevent rot.
Don't be alarmed if your plants look like dead sticks when they first arrive. This is normal and is not a cause for concern. Do, however, look for damaged or rotten root sections, and make sure to trim these away before you plant.
As you prepare to plant a bare-root specimen, keep the roots moist at all times while they are exposed.
If the roots dry out, you may very well lose the plant. Many experts recommend soaking the root zone of a bare-root tree or shrub in water overnight to fully hydrate the roots before you plant them. And make sure to water the plants thoroughly in the ground until the first new greenery appears.