Two events are independent if knowing one of them occurred tells you nothing about the probability of the other. Two fair coin tosses are independent; the weather in two neighbouring towns on the same day usually is not, because both are influenced by the same larger weather system.
Most of the simple “multiply the odds together” calculations behind dramatic coincidence claims silently assume independence between details that are, in reality, linked by shared culture, geography, timing, or cause. Checking that assumption — not just doing the multiplication — is step 8 of how to evaluate a coincidence claim.