When two things clash, they run violently into each other, often with an accompanying loud noise. The percussionist in an orchestra has the enviable job of making two cymbals clash together.
Kids clash when they run into each other on the playground, but they can also clash through a strong disagreement: "My cousins always clash when it comes to deciding what movie to watch after dinner." Also, your shirt might clash with your pants, if the colors or prints simply don't go together. Clash is imitative — it sounds like its original meaning, "make a loud, sharp sound," and may be related to the words clap and crash.