First of all, I would point out that this quote is not definitively attributed to Franklin. For example, I have seen this quote attributed to Poor Richard's Almanack and it is certainly not there.
Be that as it may, the meaning of this quote is that people will, if they are given the chance, vote to give themselves money even if it means ruining their society. This thought is somewhat consistent with the thinking of many of the Framers of the Constitution. They worried that the common people would use democracy to pass laws that would help them financially even if those laws would hurt the country as a whole.
In modern times, you could argue that American attitudes towards Social Security and Medicare bear this idea out. Americans seem unwilling to tolerate the idea of cuts in either of these programs even though the programs are the major reason for the financial problems that the government will face in the long term.