Bourdieu does this through his 3 forms of 'capital'. The normal usage of the term capital relates to currency, or the tools we use to navigate through society. Bourdieu extends this concept to include 'social capital', 'cultural capital' and 'economic capital'.
'Social Capital' - the social connections we have. 'Its not what you know, it's who you know' (famous phrase which illustrates this form of capital)
'Cultural Capital' - the culture which is embodied within us through socialisation acts as a form of capital. This implies that there are certain cultural attributes which are superior to others; such as an interest in the theatre or literature. It also extends to ways of speaking, dress sense etc. which are all a reflection of culture.
'Economic Capital' - Money.
It is Bourdieu's argument that education in contemporary society can never be thought of as 'meritocratic' (the idea that everyone has an equal chance of success, and it is hard work alone that determines this) because the amount, and the quality, of each of these types of capital has a significant bearing on your chances of success in education. For example, middle or upper class children's parents are more likely to have connections within the education system to help their children get into the best schools, or get extra support (Social Capital). Middle and upper class children are also more likely to speak, write and dress in a manner which is deemed superior due to the way they have been socialised; leading to work which is marked more favourably, and better relationships generally with teachers (Cultural Capital). Finally, and perhaps the most obvious, 'Bourgeois' parents have the economic capital to pay for the best schooling and perhaps private tutoring.
This shows that in modern society the odds of success are always tilted in favour of the upper classes; which can be backed up by statistics on the issue.