The yeti is a creature of the Gloom. While there's a yeti on your lands you can't do actions around him (including designing actions). In order to banish a Gloom Yeti you need to hit him 6 times each time costs one energy. Once the yeti is gone you can continue do what ever you like, as long as there are no more beasties on your land. A yeti might appear when working on frozen trees or frozen rocks.
The Gloom Yeti sometimes drops: