Monster Musk was used by the Wild Monster Baiter to attract monsters to your base. The more you use the Baiter, the more musk will be used. 1 musk = 1 housing space. The Baiter is mostly used for testing base defenses, as described on its page. It may have looked like bottled goo when first seen.
Note: The Baiter sends out monsters of your level, so if your Pokey is level 6, instead of using 10 Monster Musk, it would only use up 7. This is because a level 6 Pokey only takes up 7 spaces.
Getting Monster Musk
When you first build your Wild Monster Baiter, you will get a full supply of musk. When expended, musk will slowly regenerate again. Previously, shiny could have been used to repurchase musk, but the later updates to the game provide an unlimited quantity of musk.
Note: Due to a recent update, Wild Monster Baiter now has unlimited storage of Monster Musk on Facebook and Kongregate. Because of that, all the Shiny offers for getting Musk were removed on Facebook and Kongregate. This option still exists on other websites.