Yes, you can jailbreak your Apple Watch. However, the process is a bit different than jailbreaking other iOS devices. Instead of using software, you need to use an exploit that targets a flaw in the Watch's security system. This exploit is called checkm8 and was discovered by hacker axi0mX.
Once you've jailbroken your Watch, you'll be able to install custom apps and tweaks that are not available through the App Store. You can also customize the Watch's interface and make it work the way you want it to. Keep in mind that jailbreaking voids your warranty, so proceed at your own risk.