This week's contest on Twilio for Non-Profits aims to help nonprofits implement voice solutions using the Twilio API. The winning application will receive $500 in Twilio credit and have the opportunity to make a positive impact on various causes, such as education, animal welfare, and breast cancer research. To get started, contestants can explore ideas such as building a donation system or creating a platform for connecting people with similar interests. Nonprofits in need of voice application support can also reach out to Twilio for assistance, including access to resources like Google Checkout and NTEN's technology expertise.