Why does the profit reaches its maximum value at the equilibrium point?
The point where MB = MC is the largest Net Benefit available for a given product.  Therefore, any additional benefit has a lower level of benefit than at equilibrium, and the costs increase at a higher rate than at equilibrium.  In the context of supply and demand, this is where the two lines cross.  But if you think about it in terms of diminishing marginal benefit, and increasing marginal costs then you can see why it is beneficial to product where the largest net benefit occurs.

The following graph is from Markets and the Environment by Keohane and Olmstead and deals with abatement costs, but it is the one graph I think about when someone asks this sort of question because it provides a good example.

As you can see from the graph, the largest net benefit is the furthest distance between the benefit and cost curves.  If you were to take the derivative of each of these functions, you would get linear supply and demand lines, where the largest net benefit is the cross section of the lines (as you can see in the graph below).