As a ScrumMaster, you introduce the metaphor of Chickens and Pigs to help your team understand that Scrum meetings are for them because they are the ones who commit to the Sprint plans they make. Whereas a chicken, as Michael Vizdos explains, is someone who has something to gain by the pigs performing and does do not contribute to getting things done. Of course, all the Scrum roles including Scrum Team, ScrumMaster and Product Owner are considered to be "pigs" who take responsibility for making their process visible and engaging with "chickens" to get feedback on what they produce.
I'm blogging about this because I recently ran a release retrospective for three Scrum teams working on the same product. I was surprised to hear team members raise a number of worries about "chickens" in the pre-work surveys. When I invited the team to work in groups to draw pictures of what it was like working on the project, chickens also featured in some of their pictures (one headless chickens at a crossroads and another big chicken waiting at the top of a stairway moving backwards with a pig struggling up it). Something seemed strange about this and not healthy.
When the development manager followed up with me afterward, I told him that I was surprised to find a team using chickens/pigs language so much---especially as they were not new to Scrum. My opinion is that the chickens and pigs metaphor helps a team understand who talks at the Scrum meetings when they are starting out. These are not really roles to be performed with specific responsibilities so not a useful concept for the team to keep using.
Calling people animal names is likely to offend and tends to dehumanize the sitution. My opinion is that a Scrum team should be trying to build bridges with their stakeholders rather than labeling them as "chickens". There will be people outside the team who need to have some visibility into the work of the team. Take time to build a Stakeholder Map with the whole team and get to know who everyone is (without labeling the pigs or chickens). Likewise ensure that team get to meet stakeholders and hear their feedback firsthand at Sprint Review.
There are rare situations where you encounter a "chicken" who wants to get a bit too involved. How can you handle this? Often it's a case of educating them in the basics of Scrum so they understand when it's appropriate to share their opinions and ask for information. Mark W. Randolph lists some additional things you can try for talking chickens - I'd add treat metaphors as ways to introduce ideas not roles to be reinforced ever after.