Symbol of our faith.
The flaming chalice is the symbol of Unitarian Universalism, yet many if not most UUs cannot tell you the origins of the chalice (for a full history, check out this link). This indicates a lack of strong sense of identity to me, which is caused by lack of emphasis in our regular spiritual practice. Every UU should be able to tell you the origins of the flaming chalice symbol, and should have a ready answer as to what it means to them. And not because that is a "requirement", or because I believe it is something all UUs "should" do, but because if we are truly practicing our faith, living it, understanding its meaning, and identifying with it, we would know these things as a matter of default.
"The chalice and the flame were brought together as a Unitarian symbol by an Austrian artist, Hans Deutsch, in 1941 as part of the Resistance to Nazi persecutions. The flaming chalice, like our faith, stands open to receive new truths that pass the tests of reason, justice and compassion. The lighting of the chalice marks the beginning of every service."
- from "Guide For the Curious Newcomber, published by the Unitarian Society of Northampton and Florence, September 1, 2007
The only thing I would add to this is to note that "modern chalice designs often incorporate two overlapping circles which, for many people, represent our Unitarian and Universalist heritages." (see UUA website for full text.)
To me, the chalice signifies receptivity to new ideas, to growth, to change. The flame signifies light, hope, faith and love.
For a large gallery of chalice images and clip art, go here. Here's a few examples:
created by Steve Bridenbaugh
created by Jeanne Sanzchez-Bell, Kenosha, WI, Bradford Community Church UU
created by T.A. Ingram, UUFM, Mobile, AL