When something has urgency it requires speedy action. If your weather report is flashing red and predicting a hurricane with record rainfall, that forecast would give some urgency to getting that hole in your roof fixed.
Urgency comes from the Latin urgere, which means "press, or drive," and it's related to the English word urge. If there's urgency to a situation, it's a pressing issue and you have to respond quickly! Urgency also means an earnest and insistent need. When your friend calls and tells you, "Get into the basement, the hurricane is coming," there would be an urgency in your friend's voice that would make you scurry downstairs to safety.