A growth medium or grow medium is whatever it is that you're growing your cannabis in, whether that substance is soil, perlite, coco coir, rockwool, water, etc.
Your marijuana plant will thrive as long as the roots have room to grow and have consistent access to fresh water, oxygen, and the proper nutrients. There are a variety of ways to satisfy all these needs of a weed plant while growing.
Growth Mediums for Marijuana
Soil or compost is one of the most popular growing mediums for marijuana plants becauseit is natural, easy to use, and available everywhere. If you decide to use soil, try using a sterilized, loose, non- peat based potting compost. I recommend mixing your soil 50/50 with a soil conditioner like perlite which will provide drainage and keep higher amounts of air/oxygen in the soil.
Soilless mediums such as rockwool, perlite, vermiculite, and coco coir also all make great marijuana growing mediums. My preferred method for beginning growers is to start out their plants with a mixture of half perlite and half coco coir and then water their plants by hand. I have written a detailed tutorial on how to grow marijuana with perlite and coco coir. Soilless mediums are great because you can treat your grow almost the same as soil only you just feed them all their nutrients in the water (hydroponically). Because your plants are getting the nutrients delivered directly to their roots, you will often get quicker growth and higher yields when growing hydroponically. Another advantage of soil-less mediums is that you are less likely to have problems with mold or bugs.
Other hydroponics have you grow your cannabis directly in water or even in air. The style of hydroponics which seems to get the highest yields is a method known as bubbleponics or a top-fed Deep Water Culture (DWC) system. I have a tutorial which will show you how to grow your marijuana plants using the bubbleponics method.