Question:   What's the difference between the concentration and activity of a solution?

Answer:

The concentration of a solution is a measure of how much stuff is dissolved in a liquid.  It's easy to figure out a concentration, because you can just measure the amount of solute that you're putting into the solution to find the molarity, molality, or whatever concentration you're trying to find. The activity is a little harder to pin down.

Activity is an effective concentration, based on something called the chemical potential.  Much as the Van der Waals equation describes real gases in place of the old PV=nRT, activity can be used in place of concentration to describe the behavior of real solutions vs. ideal solutions.

For information about the thermodynamics behind activity (it's related to fugacity, if that helps), take a look at a college-level physical chemistry text.