It's more than a plant with stickers. To a botanist it is a plant that has certain characteristics that place it in the family of plants known as the Cactaceae. A unique feature of cacti are areoles, small areas on the stem which contain spines. Areoles are also the places where flowers, new stems, or roots arise. A cactus is a perennial, that is it can live for many years.
Most cacti are without leaves.
The stem is fleshy or succulent and contains water-storing tissue. These features allow the plant to withstand periods of drought, which is a common occurrence in the habitats where cacti grow. All cacti can be called succulents, but not all succulents are cacti. In addition to the Cactaceae, succulents occur in the lily, milkweed, daisy, stonecrop, and about 45 other plant families. The vast majority of cacti live in desert and semi-desert habitats.