The Twilio Developer Contest is a bi-weekly challenge that encourages developers to build apps using the Twilio API. The contest aims to help people get organized and productive in the new year by building an app that helps with tasks such as task management, goal setting, and bug tracking. One winner will receive a Kindle Fire for submitting the best entry. The contest has a deadline of January 15th and requires submissions to use Twilio API. Developers can find inspiration from previous winners' apps and participate in forums or submit their ideas through a dedicated form.