The search algorithm used in AutoDock is not just looking at one possible solution of one candidate drug molecule (ligand) but is actually evaluating many possible solutions at once. The spheres show places where the best drug molecule to HIV-1 protease dockings have been calculated and the color shows how good they are.
AutoDock is trying to find the best way that the current ligand, the one your agent has downloaded, can fit together with the target HIV-1 protease. You can think of the ideal drug we are trying to find as a "key," and the HIV-1 protease as a "lock." Unlike keys in the real world, however, many drug molecules bend to change shape. In this respect, molecules are like a dancer's body; the same body is able to adopt many different poses and shapes. Unfortunately, we do not know what shape a candidate drug will adopt until we try millions of different possibilities and then select the best one.
To find the best fit, we are using an algorithm. An algorithm is just a recipe, a list of ingredients and instructions on how to do or make something. We are actually applying the principles of evolution in our search algorithm to find the best way that our candidate drug molecule would best fit together with the target, HIV-1 protease. Like evolution in the real world, we have a "population" of possible solutions to the problem.
This is what you are seeing when you look at the different colored spheres dotted around the white ribbon diagram. The colors correspond to the same colors of the crosses in panel B. Those representing more negative energy are considered better dockings. AutoDock uses a representation for each of these ligand dockings that says where the ligand's center is, what its orientation is, and what shape it has currently adopted. AutoDock applies genetic operations on the representations of random pairs of ligand shapes to generate two new representations and hence potentially better solutions. You can see how well AutoDock is doing by looking at the graph in panel C.