Three big characteristics of surrealism are association, symbolism, and a celebration of the irrational.
Association is the connection people can make between different objects, people, or ideas. In surrealism, artists often make unexpected associations to surprise the viewer. A simple example would be the short film Entr'acte, which indulges in free association of several bizarre and seemingly unrelated images.
Symbolism is also a common element of surrealist art. Surrealism took inspiration from dreams and dream analysis as popularized by Freud. In such analysis, images and figures within dreams take on heightened symbolic meaning. For example, Frida Kahlo's paintings are packed with symbolism. Self-Portrait with Thorn Necklace and Hummingbird features several symbols linked with the idea of rebirth and resurrection, such as butterflies and a necklace of thorns which act as a play on the crown of thorns forced upon Christ before the crucifixion. Some of the symbolic images are also significant to Mexican culture, such as the hummingbird around Kahlo's neck, which symbolizes good luck.
Surrealism also tends to celebrate irrationality. This was originally intended as a reaction to the emphasis on rationality within western culture as a whole. Surrealist art is often accused of making no sense due to its emphasis on the nonsensical and bizarre. Franz Kafka's literary work often focused on the irrational in both human behaviors and narrative events. Gregor Samsa turning into a large insect in The Metamorphosis is certainly bizarre, but so too is the hunger artist starving himself because he does not enjoy food in "A Hunger Artist."