"Perennials" are plants with soft or semi-woody stems that live for more than one year, usually with their top growth dying back in fall or winter and returning the following spring from roots that survive underground.
More specifially to paraphrase Merriam-Webster, a perennial plant persists for several years, usually with new stem and leaf growth from a part (root, rhizome, trunk, etc.), that lives over from one season to another. Horticulturists and gardeners use the term "perennial" for herbaceous plants as opposed to trees and shrubs. Annual plants, on the other hand, usually only live for one growing season, during which they flower, set seed and then die. A third plant type, referred to as biennials, are plants that typically only live for 2 years, producing foliage the first year, then flowering and producing seed the second year.
While most perennials lose their foliage in the fall and go dormant in the winter, there are those that are evergreen and others that go dormant in the heat of summer. Some will be evergreen only in mild winters and these may be referred to as semi-evergreen. Be aware that a plant that is perennial in one climate (usually its native climate) may be an annual in significantly colder climates.
The USDA has set up a system of Hardiness Zones dependent on winter low temperatures to help growers determine if a plant will be hardy in a given area. (There is also a Heat Zone map, but it is not as frequently used.) To determine your zone refer to: USDA Plant Hardiness Zone Map. It is a good idea to check which USDA Hardiness Zones the particular plant you are looking at can tolerate. You may sometimes be able to "stretch" the zone for a particular plant if you have an unusually protected or exposed area. We only grow plants that we believe will be hardy to at least Zone 7, unless we note otherwise. We list the hardiness zones for our plants as best we know from experience or published information.