Vested interest is not a term that often appears in textbooks, but is one that everyone should learn - if only because it helps us understand news about various controversies. You are said to have a vested interest in something if you stand to lose or gain from changes to that something.
For example, if you are a public housing tenant, you are more likely to support a continuation of government policy to build subsidised housing for low-income families and to maintain low rents at public housing estates.
Note that I am being cynical here. Very strong arguments could be made for or against the policy of providing affordable accommodation to the masses, and public housing tenants are not the only ones who have a vested interest in the issue.
At present, about half of Hong Kong's population lives in public housing estates. Low rents and secured tenancies at these estates provide a bedrock of social stability. But these estates are a drain on public resources as the costs of building, maintaining and managing them cannot be covered by the low rents. There is also widespread abuse by tenants who refuse to vacate their units after becoming well-off. What I am trying to say is that human nature is such that one is more inclined to protect one's own interest at the expense of the public interest. That explains why those who stand to benefit from a policy are more likely to support it than those who do not, regardless of the merits of the policy.
Hence, one way of looking at public housing groups' demand for the government to keep building public housing estates and maintaining rents at low levels is that they want to protect their vested interest in enjoying these benefits.
On the other hand, developers' call for the government to scale back the public housing programme could be explained by their underlying desire to enrich themselves as people would be obliged to buy or rent the flats they build. Many private home owners who pay taxes but get no housing benefits from the government are also in favour of scrapping public housing because they feel it breeds welfare dependency and is a waste of public money.