It means you have a vested interest in the outcome of the issue. Usually one resolution will benefit you, or the other will adversely effect you. Therefore you are likely to show bias towards that side that favours your position in relation to the issue.
For example, a game hunter involved in the issue of duck hunting is a stakeholder in the issue because the outcome will directly effect him/her. It is likely a hunter will show bias in favour of duck hunting as this would be the favourable outcome of the issue for them, whereas the prohibition of duck hunting would have a negative impact.
Thus when analysing a written piece where the writer is a stakeholder in the issue, it is important to recognise that the text may not be very balanced as the writer only wants to persuade the reader to agree with one side of the issue (the side they are one). Even if they try to mask their bias with a seemingly balanced argument, someone with a vested interest in the outcome of the issue will almost always try to present their side in a more favourable light compared to any alternatives.
Again, a game hunter writing an opinion piece may try to appear objective and reasonable by presenting both sides of the issue, however, they may only bring up their opponents arguments so that they can rebut them, or they may only choose selective arguments that are weak or flawed to insinuate to the reader that their side of the issue is superior.