This phrase isn't something mythical or religious. Rather it reflects the totality nature of Martial Arts. Training the physical movements (Body) without taking the time to study and embody the rest only gives a student half the picture. It'd be like trying to ride a bicycle without the chain to connect the pedals with the tires.
Mind. Any trained fighter will tell you there is more to the fight than just throwing a punch. One must come mentally prepared. Then even before the first strike, there is a whole psychological battle that occurs between the opponents. This mind concept also extends outside of the arena. It has been proven by a number of studies in a variety of activities from test taking to football that visualizing what you're about to do is a powerful technique to improving what you do.
Developing the mind is a long process that begins with the most simply question that any two-year-old can give you, "Why?"
All these simple questions build the student's understanding of the Arts and their abilities to visualize what they are doing.
Spirit. This is a much harder aspect to capture and often teachers will shy away from it in this day of political correctness and fear of religious retribution. This, however, shouldn't be something we are afraid to express and share.
Spirit speaks to why we study Martial Arts, what is in our hearts and compels us forward. If our hearts are filled with hatred, a desire to hurt, then so too will our studies be limited and the true embodiment of the Arts will be lost. If our drive comes from titles or belts, then we have missed the meaning behind why we're studying. If our eyes are set on trophies and medals, then this is all we will be able to see and miss the rest of the strength the Arts provide us.
Training more than just the physical, the Body, is key to truly understanding Martial Arts.