Imagine you have a friend who is always willing to help you out when you need it. This friend is like an insurance company when you get sued - if someone sues you, your friend will come to your defense and help protect you. This is called a "duty to defend."
When you buy insurance, you are basically asking this friend for help in case something bad happens to you (like a car accident). If someone sues you because of that accident, your insurance company will step in and take care of things for you - they will pay for a lawyer to defend you in court, and they will cover any damages you might have to pay (like the other person's medical bills).
But there's a catch - your friend (the insurance company) will only step in if the lawsuit is related to something that is covered under your insurance policy. So if your insurance policy only covers car accidents, and someone sues you for something totally unrelated (like stealing their bicycle), your friend won't be able to help you out.
The duty to defend is basically the insurance company's job to come to your defense when you get sued for something that falls under your policy. They are promising to be your friend in times of trouble, and to protect you from harm.