The corolla is a term that means all the petals of the flower. However, in order to understand what the corolla is, you need to understand that what looks like a petal is not always a petal. In fact, some flowers don't even have petals. This might seem confusing, but once you understand a little more about basic flower structure, it is easy to understand what parts of the flower make up the corolla.
Petals are soft, thin, typically brightly colored, modified leaves. Petals form whorls around the reproductive organs of a flower. The petals are usually the second whorl and have sepals surrounding them. However, not all plants have petals. Some, such as hellebores, have petaloid sepals, which means that the sepals are modified to look like petals.
As said earlier, all the petals of the flower make up the corolla. In the picture of the rose, the corolla includes all of the pink petals, but does not include the green sepals (described below) nor does it include the reproductive parts of the flower such as the stamen and pistol.
The sepals are part of the outer whorl of the flower. They are usually green, but not always. For example, day lilies have colored sepals. Like the corolla, they are non-fertile parts of the flower. Although they are not part of the corolla, the corolla and the sepals of the flower are known as the perianth.
The calyx includes all the sepals of the flower. It is the protective cover of the flower that once enclosed the bud.
Tepals is a term traditionally used when flowers do not have distinguishable sepals and petals. A good example of this is the tulip, where both the inner and outer whorls appear the same.
The perianth is the outer part of the flower and includes both the calyx and the corolla of the flower. Basically, the term is used to refer to all the non-fertile parts of the flower. This term is often used when the calyx (sepals) and corolla (petals) are hard to distinguish from each other.