Succulent is the term used to describe the abilities of certain plants to store water. Not all succulents are created equal, but they all have this property to a greater or lesser degree.
Some 'succulent' plants have modified leaves, such as Epiphyllum, the Orchid Cactus.
They live high up in the top of jungle trees, and get moisture from rain showers, which runs down the branches of the trees to where they root in the crook of a trunk.
Others have evolved to be almost completely adapted for water storage - think cactus here. They are a stem, with no leaves that we can recognize, although the thorns are actually modified leaves.
They can store water drawn up by the roots from the infrequent rainstorms in their native habitats, and live off that stored moisture for years, in some cases.
Some other plants could also be called 'succulent' even though they don't look like it.
These are plants that are drought tolerant due to their roots, which store water in a tuber or bulb. These are commonly grown in our gardens.
You will recognize Hemerocallis, the day lily here, as well as many other plants - Aloe has the same kind of roots, so it's got double insurance for water storage (leaves and roots).
Think of the word succulent as just a description of what these plants can do with very little water; plump up their cells to store it for later when they really need it.