symbolize
To stand for or represent another idea or thing.
To symbolize means to represent or stand for something else, usually something bigger or more abstract than the symbol itself. A dove symbolizes peace, a red rose symbolizes love, and a lion symbolizes courage. The symbol and the thing it represents aren't the same, but they're connected in a way that people recognize and understand.
Symbols work because humans agree on what they mean. When you see a heart shape on a Valentine's card, you instantly think of love, even though the shape doesn't look much like an actual human heart. When a country's flag flies over a building, it symbolizes that nation's presence and authority. In The Lion, the Witch and the Wardrobe, Aslan symbolizes goodness and sacrifice, representing ideas that go beyond just being a character in the story.
Writers and artists use symbols constantly. A storm in a novel might symbolize inner turmoil or conflict. A journey might symbolize growing up. A character's old, worn teddy bear might symbolize childhood innocence or comfort in difficult times.
The related nouns are symbol (the thing doing the representing) and symbolism (the practice of using symbols or the meaning behind them). When your English teacher asks “What does the green light symbolize?” in The Great Gatsby, she's asking what bigger idea that green light represents.