It's a word that describes someone who is quick to get upset or angry, often over small things. Here are some synonyms:
* Irritable
* Grumpy
* Cross
* Short-tempered
* Touchy
For example:
* "My grandmother is getting quite tetchy in her old age."
* "He was in a tetchy mood all day because of the traffic."
* "Don't bother him; he's been tetchy ever since he lost his job."