Transpiration is the evaporation of water from the leaves of plants. In this way they contribute to the water cycle.
Here's how it happens: a plant sucks up groundwater through its roots and up into its leaves. The leaves use light energy to make food for the plant, requiring water in this process. This is called photosynthesis. After the food is made, water is released through the plant's leaves to evaporate into the air.
A plant requires transpiration for several reasons. By sucking up water from the ground to the leaves transpiration also helps suck up the nutrients the plant needs from the ground. Transpiration is also vital for the plant to make food, and also helps to cools the leaves down - similar to how humans perspire or sweat to stay cool!