Cleave is one of English's most confusing words because it means two opposite things.

1. To split or cut something apart, usually along natural lines. A logger cleaves a piece of wood by driving a wedge along its grain, splitting it into two pieces. A butcher cleaves meat with a heavy knife called a cleaver. When rock cleaves along a fault line during an earthquake, it breaks apart cleanly. You might also hear someone say a boat cleaves through the water, meaning it cuts smoothly through the waves.
2. To stick firmly to something or someone. In old-fashioned language, you might read that someone cleaves to their beliefs, meaning they hold onto them strongly. The phrase “cleave unto” appears in traditional wedding vows, meaning to stay loyal and attached.

When you encounter cleave in your reading, the context will tell you which meaning fits. If someone's cleaving wood, they're splitting it. If they're cleaving to their principles, they're holding on tight.