Worse means "not as good as something else" or "changed negatively," like a sore throat that is getting worse, meaning it hurts more now.
Worse comes from the Old Saxon word werran or "to entangle, compound." To compound is to add to, so if troubles, complication, or anything else that entangles are added to a situation, it will get worse. Remember that worse is used to compare two things, such as "now" and "before," while worst compares three or more things. You might use worse than yesterday, but this doesn't make it the worst cold you ever had.