Hydroponics is the art of growing plants without soil. When most people think of growing marijuana hydroponically, they think of growing their plants with their roots suspended directly into water with absolutely no growing medium. However, this is only one type of hydroponic growing. There are several variations including growing your plant in a soilless medium such as perlite/coco coir and then watering your plants every day, which is not very different from growing in soil.
Example of cannabis plants grown with roots in reservoirs of water (hydroponics)
The advantage to growing hydroponically is that you deliver all the nutrients the plant needs right to its roots. In soil, the roots have to seek out and extract all nutrients, but with hydroponics, you take the work out of finding nutrients so the plant can focus more of its energy on growing bid and making flowers/buds. Therefore you will end up with much faster growth and higher yields than if you grew your marijuana plants in soil.
Hydoponics can be very simple or very complex, depending on your set-up. I recommend with starting with a method that's on the simple side, and then trying a more complex method once you have a little experience under your belt.
If you would like to learn how to grow weed using bubbleponics, GrowWeedEasy.com has a detailed tutorial. Growing with bubbelponics has one of the highest yields of any cannabis-growing technique.