Cro nailed it...
To add to his answer, The Garland turn is generally started from the sideslip position with the board across the fall line. The rider should shift their weight to their front foot and relax the front foot so as to release any uphill edge pressure. This allows the nose of the board to begin to slip downhill and allow the board to begin to move. The rider allows the nose to almost point straight down the fall line then they will use the front foot to pressure their edge and twist the board to steer it back across the fall line. They can either come to a complete stop and repeat or they can learn to slow down and release again.
This teaches them to torsionally steer the board with the front foot as well as allow them to gain experience at turn initiation without fully committing to making a complete turn. Garlands should be done heelside and toeside. Once the rider is comfortable allowing the board to point straight down the fall line for a couple of seconds before steering back across it, they are ready to make completed linked turns.
The main reason these are so much better than falling leafing is because this exposes the new rider to being on the board with it pointed down the fall line and steering it back out of this position to slow down and stop. With the falling leaf, most new riders fear letting it point too far down the fall line and this creates a mental block that can be a bitch to overcome especially if the rider is timid or fearful.
As Snow Motion said, basic snowboarding is ridiculously simple. The biggest obstacle to learning to link turns is simple fear and hesitation. The Garland turn gets the new rider to face their fears and overcome them quickly whereas the falling leaf actually enhances their fear of pointing the board down the hill. The Garland also teaches the rider to ride their board directionally instead of the constant switching between regular and goofy. This switching back and forth at this stage of learning to ride is a major inhibitor of progression and the new rider may go for a very long time with no clue as to whether they are regular or goofy.