An attempt at an explanation...
...from an American that is disappointed with most American politics.
Liberty is meant as you say, personal freedom. However, it is the debate over what the "constraints of society at large" are that gets otherwise sane people all frothy.
Examples. On the "conservative" end, there are few to no constraints on business, land use, gun ownership, etc. But that same demographic endorses constraints on civil union, scientific progress, financing the government, and who can become a member of society. These constraints are usually argued on the basis of Christian morality, and when Christian morality doesn't agree, they are argued instead on the basis of nationalism. Note that when I refer to Christian morality in this context, I mean mostly the evangelical interpretation thereof, which unfortunately leaves out a lot of the "love thy neighbor" lessons. To summarize, this mindset specifies that the individual must prosper, and that society will benefit if this is allowed to occur. However, the individual must prosper according to a set of moral rules that have been tweaked a lot in the last hundred years or so.
On the "liberal" end, the constraints on the individual are largely removed, and placed on society instead. For example, gay civil union is legal and drugs like THC are legal (but heavily taxed). However, due to heavier regulation on society as a whole, personal liberties are stifled by laws such as the DMCA. Small businesses suffer under one-size-fits-all legislation designed to reign in the larger corporate behemoths. These constraints are mostly argued on the basis of advancing society, or on the basis of protecting society from itself. To summarize, this mindset specifies that society can best advance when managed from the top, and that layers of organization and regulation will insure compliance. However, by limiting the resourcefulness of the individual, the desired progress is stifled.
Both sides are hypocritical. And thus I find both sides completely disappointing. Those of us caught between the extremes try to pick and choose the best of both sides, but American politics is extremely polarized, so there is rarely a viable centrist option.