When things go from terrible to even more terrible, they worsen. If your sore throat worsens, you should call the doctor.
If something gets worse, you can say that it worsens. So if the rain that started as a misty drizzle begins to grow torrential, threatening to ruin the picnic you've planned, the weather worsens. And if there's less money in your piggy bank every day, your financial situation worsens. The verb worsen shares a root with war, the Old Saxon werran, meaning "to entangle."