What is involved in "making society better"? What do we have in mind when we aspire to improving society? I suppose there are several things we might mean by this idea. Superficially we might say that a society is better off when its members are better off; but is there more to the story? There seem to be several different lines of thought to pursue.
First, we might have a small number of dimensions of goodness in mind -- something like a social welfare function -- and we might understand social progress as aggregate improvement with respect to these dimensions of welfare. Social progress is defined as "aggregate improvement in quality of life for the population" (income, health status, freedom), and it is achieved through a series of steps in which one or more of these measures is improved. This definition is potentially more complex than a utilitarian moral theory, but it shares the basic structure with utilitarianism. It defines the good of society as the sum of the goods of individuals in society. (We might also have a theory about the processes through which these improvements need to take place; for example, we might say that all improvements need to be Pareto-improving: making some better off without reducing the welfare of anyone.)
Second, we might have a list of specific current social defects in mind -- the widespread fact of urban homelessness, the incidence of childhood obesity, or the incidence of violence in society -- and we might define progress as the reduction or elimination of these defects. Social progress is the result of sequential reduction of social harms.
Third, we might have a set of moral-structural theories in mind: fairness, equality, democracy, self-determination. And we might define progress as a reform of institutions that increases one or more of these features of society. We might be thinking here along the lines that Rawls suggests in talking about imperfect justice; improving society means reforming unjust institutions and practices. Or it means reforming institutions that unnecessarily interfere with citizens' freedoms. Or it means reducing the ways in which institutions treat citizens unequally. This differs from the standard-of-living definition, in that it looks at the characteristics that need to be addressed as relational and systemic characteristics, not simply aggregates of the wellbeing of the individual members of society. A society is better when it is more just or more free. Here we might find ourselves in a position of saying that "Society A is in a better position than society B, even though citizens of B have a higher level of material wellbeing than those in society A." Apartheid was a particularly egregious example of a systemic defect in a society, and it required fundamental structural change to improve the apartheid society. Current discussions of democratic institutions fall in this category; the idea is that institutional reforms can create new procedures that better embody the ideals of democracy.
Fourth, we might have in mind the important point that social institutions and practices work in very specific ways and have differential effects on different groups of people in society. So we might have in mind the idea of improving the workings of the basic institutions of society -- improve their effectiveness and efficiency, or improve their equity in terms of their effects on different groups. This is analogous to the goal of "making the air transport system better": we look at the goals the system serves and the practices and procedures through which it does this, and we try to design better procedures to accomplish the goals of the system. We might notice that the environmental regulations governing the siting of hazards tend to disfavor poor people, and we might try to make them more democratic. Or we might notice that land-use permitting processes are very cumbersome in many cities, thus discouraging new and productive uses of land, and we might try to change them in the direction of greater efficiency. Each effort could be described as "making society better."
Fifth, we might try to locate "social progress" entirely in terms of the wishes and preferences of the members of society. This is a liberal and democratic definition of social wellbeing: the wellbeing of society, and what counts as an improvement in social wellbeing, is entirely specified once we know what the citizens prefer. So on this approach we might say that "social progress" is entirely procedural: a set of changes represent progress just in case they were arrived at through a fair and equal process of collective decision making.
An important issue that arises in thinking about social progress is the question of myopia and design. Think of the analogy with the evolution of species: natural selection is a myopic process in which each change is fitness-improving, but there is no longterm plan for what the species will eventually look like. Coming up with a better bicycle, on the other hand, is usually the result of a far-sighted design process, in which the architecture of the bicycle is reconceived so as to achieve certain design goals. The thing about a myopic process of improvement is that it is possible to get trapped in a local maximum, unable to take one step back in order to achieve a higher nearby equilibrium. (Richard Dawkins describes this possibility in Climbing Mount Improbable.)
So what about social progress: should we think of social improvement as the net result of many small, myopic reforms; or should we think about it ideally as the result of a comprehensive policy design process? To what extent are we in a situation of improvement resulting from a large number of small adjustments, versus the possibility of large designed reforms leading to discontinuous jumps in quality and equity? The constraints of democracy strongly suggest the former rather than the latter. Building legislative and democratic majorities for change seems to imply piecemeal reform and a degree of myopia. It is difficult to see how a comprehensive, multi-decade plan for social reform could be implemented and sustained. (Adam Przeworski considers some of these issues in Democracy and the Market: Political and Economic Reforms in Eastern Europe and Latin America.) So piecemeal and gradual reform on several fronts may be the best we can do.
Generically the concept of reform fits into these ideas very tightly. Reforms are intended to improve the social situation in one way or another; and the cumulative effect of an extended series of reforms may be a significant enhancement in equity, democracy, equality, and quality of life. But two things are usually true: first, reforms are generally selective and partial; and second, the cumulative effects of an extended series of reforms may lead to outcomes that were never anticipated. A reform process is not a utopian process: it is generally not guided by a comprehensive vision of what the ideal society ought to look like, and the results of reform are generally pragmatic and limited rather than sweeping and socially transformative.
(The image above is drawn from a manual on forestry management in Karnataka, India (link). It depicts a sequence of social systems of land use governing farm land, cattle husbandry, and forests. The middle panel represents degradation of the system and the worsening of the standard of living of the population; the final panel represents the improvement of the system of land use and a major step forward in the standard of living as a result of a major legal reform, confined cattle and protected regenerated forests.)