You hear the term “vested interest” in many contexts, but when looking at financial matters the definition is fairly specific. Either your vested interest  gives a party the right to gain a specific asset , now or in the future, or it indicates a stake in a particular action wherein you expect to gain a benefit.
Pension plans often require a certain vesting  period. This is the time an employee must spend with a company to qualify for specific retirement benefits. The length of the vesting period varies, and sometimes a partial vesting occurs at one point while full vesting occurs at another time. There may be restrictions related to the total amount withdrawn annually as well.
In the case of a vested stake, the outcome of the situation affects the party involved. A classic example would be: if you loan someone money to get a business off the ground, you would have a vested interest in seeing the business succeed so you get your investment back, preferably with a profit .
This situation describes not only a financial vesting, but a personal one as well, as ego is involved. No one likes to think that they have taken an unreasonable risk when investing their capital .
When relating vested interest to non financial matters, the degree to which an individual is affected by the condition often determines their level of emotional response. For example, a 15 year old would be considerably more distressed by a referendum to raise the driving age from 16-18 than someone who is 25 and already licensed.