Something that can be broken easily is "fragile". Some examples of fragile things include:

• a wine glass
• old antique furniture
• a ceramic sculpture

You can say that a person is "fragile" when they have had serious emotional events happen and they can be easily upset. For example, someone whose parent has just died might be "fragile":

He's very fragile right now, so try not to bring up anything that might upset him.

A situation can also be "fragile". For example, two countries that are often at war with each other might have a "fragile peace" which can easily be broken and return the countries to fighting each other.