Total dissolved solids is the amount of stuff (chemicals, minerals, etc)....that are dissolved in water, once the spa water has become saturated, it becomes a real bear to keep clear. You'll know when this happens, b/c no matter how much dichlor you shock your spa with it won't stay clear.
Total chlorine is the TOTAL amount of chlorine in the spa water.
Free chlorine is the amount of chlorine that is available to sanitize the water.
FREE chlorine should ALWAYS EQUAL total chlorine. If your free chlorine is lower then the total chlorine chances are good that your spa is cloudy, or you have a very pungent chlorine odor. This is what is known as a breakup in chlorine. An easy analogy would be a football team. When all of the players are working in sync together the offense moves the ball at will. Hence all of the chlorine you put in the spa is working to sanitize your spa. Now, we come to the Minnesota vikings. When randy moss takes a few plays off, the offense is not as efficient. Same thing with your chlorine, when some of the chlorine isn't available to sanitize, or is taking a couple of plays off, bad things happen. I know it's a cheesy analogy, but it helps to explain the concept a lil easier.
Honestly i wouldn't worry al that much about this. Just remember to drain and refill every 3-4 months, test your spa water once a week, make adjustments accordingly, and above all else enjoy your spa!!!