A burner that clicks but doesn’t light isn’t dangerous on its own — the igniter simply isn’t creating a spark, so no gas is being ignited. The situation to stop and pay attention to is different: if you smell gas, or if a burner lights with a delayed “whoomph” instead of catching immediately, that indicates gas has been accumulating briefly before ignition, which is worth having checked rather than continuing to use that burner.
A simple clicking-but-not-lighting burner is safe to leave alone (just don’t use that burner) until a technician can replace the igniter — but any gas smell or delayed ignition should be treated as a stop-and-call situation.