To tremble is to quiver or shake without meaning to. Your hands probably tremble when you're nervous.
Trembling is a movement, but it's not one that anyone intends to make. Someone who is extremely scared or cold might tremble all over. Older people tend to tremble more often than younger people, sometimes because of serious disorders like Parkinson's disease. The root word of tremble is the Latin tremulus, "trembling or tremulous." Certain honey bees perform a wiggly, shivering movement called a "tremble dance," which scientists believe inspires speedier nectar collection.