While there are many different forms of knitting from various regions around the world this article speaks from the Western Continental and English style perspective.
The first style we will talk about is English Style. English Style, also known as "throwing" is where the knitting needle and the working yarn are held by the left hand while the right hand simply holds the knitting needle that has all of the stitches waiting to be worked. In the English style of knitting the left hand will insert the tip of the left hand needle as appropriate for the stitch, wrap the yarn around the left hand needle in a clockwise manner, draw the yarn through the existing loop and then slide the old stitch off of the right hand needle. The right hand is simply providing stability to the right hand needle. This method is extremely useful for those who find using their right hand in any manner requiring fine motor control awkward or have limited dexterity in their right hand. The drawback to this method is you are having to stop and start each time you are wrapping the yarn.
The second style, Continental, has the work being divided between the left and right hands. The left hand is responsible for inserting the tip of the left hand needle into the stitch on the right hand needle; the right hand, which holds the right hand needle and the working yarn, then wraps the yarn as needed around the tip of the left hand needle in a clockwise manner. Now, the left hand needle draws the loop through the existing stitch and slides the old stitch off of the right hand needle. The benefit to having the right hand holding the working yarn is that you never have to have a break in your movements and provide an increase in overall knitting speed. The draw back to this method is you do need to coordinate the movements between the two hands.
Here are video's showing making a knit stitch in both styles side by side:
I predominantly utilize the Continental method of knitting. In part that is because I have a background in crochet so the distribution of work between the two hands feel natural to me. That does not mean Continental is the way for everyone. There are times when I do utilize the English Style of knitting, such as when I am doing color work.
My advice to any knitter is to try both and see which one works best for you and keep your mind open to the possibility that there may come a time when each would be useful. As I say, they're your hands so go with what feels right for you!