The entire history of the concept of cultural capital is not something I could write here, so instead I will tell one indicative story from my own experience, and then talk a little bit about how the theory of cultural capital can be used and misused.
Some years ago, I was in graduate school. More specifically, I was in a class called "Sociology of Education". It was an interesting class, because it included both the academic theory types, and a few people who were already employed as teachers who wanted further certification. One of my fellow students, a teacher and baseball coach from a suburban high school, was commenting on something we had read about class structure in America, and said that he knew plenty of people who had done well from poor backgrounds. This caused a minor and unproductive uproar in the classroom. Later on, when working in a small group with two students who were (like myself) community educators working with disadvantaged populations, they both (with predictable eye rolls) commented: "I can't believe someone would be going on with that boot strap stuff".
It is a bit unfortunate that all of us, in graduate school, at a time when we are supposed to look through ideas and examine them critically, we were dividing into camps based on easily understood narratives. Either background meant nothing, or background meant everything.
And is that attitude that muddies up the otherwise simple and productive concept of cultural capital.
Cultural capital is cultural because it is based on "soft skills", attitudes and implicit knowledge, rather than on objectively defined conditions. And is capital because it can be used to produce more assets (either tangible or intangible).
Cultural capital does not have to be looked down at in a hierarchal way. It could be argued that a person of higher socioeconomic status doesn't have more cultural capital than a person of lower socioeconomic status, but merely a different type. For example, the richer and more educated person may not have the ability to read a bus schedule. Of course, the cultural capital they lack may not interfere with their goals as much, but that doesn't mean that they somehow objectively have "more" or "better" cultural capital.
Cultural capital is everywhere, and effects everything we do. I am using cultural capital right now while writing this. I have cultural capital because I have a computer, because I know how to write, and how to use HTML. And I have cultural capital because I am sophisticated enough to know about this site, rather than trying to type out my theories as comments on a Yahoo! news article. I lack certain types of cultural capital, as well: despite years of education, I still am a bit unclear on the entire affect/effect thing.
We live in a complex world, and to do anything requires a myriad amount of skills, some of which can be taught easily, and some of which are the result of steady acculturation. To pretend that because someone has been taught a set of easily defined, tangible skills that they are on a level playing field with everyone else takes willful ignorance.
On the other hand, cultural capital isn't everything. Plenty of people do succeed, both financially and personally, even if they didn't have parents who could afford clarinet lessons. As stated above, cultural capital is not something that can be quantified in terms of "more" and "less", but rather is something that has quality: everyone has their own background, which teaches them certain skills and attitudes. Sometimes a background that at first seems disadvantageous gives skills and attitudes that are optimal for certain activities.
So without having to "pick sides", and to constrain ideas of cultural capital to an easy narrative, the idea of cultural capital becomes both very obvious, and very useful: that people's background gives them certain attitudes and implicit knowledge and skills that allow them to do other things with relative ease.