It just means to “use” caution. It is a very common way of expressing the idea “be careful.”

Hey Bianca, the word "exercise" can be used in a few other sentences as well. We might say "he/she exercised restraint" "learn to exercise patience" etc. In most cases you can replace it with "use". Exercise is a little more formal but is used often enough in educated conversation that it would sound natural in the right place. If I were warning a child, I would just say "be careful", a friend or family member "be careful" or "stay safe", but if I were warning my university professor, then I would bring out "exercise caution!" Hope that helps, J