The Twilio company has partnered with oDesk to connect developers with the necessary skills to work on Twilio-powered applications, providing project owners with access to experienced developers in a marketplace setting. Developers can find opportunities to work on such projects and get paid upon successful completion, while also receiving technical resources and support from Twilio. The partnership aims to facilitate connections between businesses and developers, promoting innovation and problem-solving through the use of Twilio's communication platform.