The term annual is applied to garden flowers that complete their life cycle in the span of one growing season. This means they come up in the spring, grow, flower, set seed and then die after the frosts in the fall.
There are many plants used as annuals in northern climates that are in fact perennial if planted far enough south where they do not experience the damaging effects of frost. These are termed tender perennials used as annuals. These include such plants as geranium, impatiens, vinca, coleus, and lantana. If one wants to save these plants from year to year, they would need to be dug up, potted and brought indoors or cuttings taken from the plants, rooted, and the resulting plants overwintered indoors.
There are a number of annuals that may act like perennials because of the large amount of seed they drop in the fall. This seed remains viable over the winter and new plants emerge in and around the area where the annual was planted the previous season. Plants like cleome, snapdragon, amaranth, cosmos, and petunia are examples.