Universal describes something for everything or everyone. Universal design is architectural design that accommodates every person. A universal remote can change the stations on all your home entertainment systems, but hopefully not at once.
The uni in universal means "one" so this word is all about "one for all and all for one." If it's universal, it applies to all cases. Like the universe itself, a universal emotion is one that every human can understand or relate to. The desire for your children to be safe and happy is universal. If you are to make a universal change in a document it means that every time the specified word appears, it should be fixed.