Participants in the PyBites code challenge are tasked with creating a Python script to compare the similarity between two Twitter users based on their recent tweets. The challenge involves retrieving the last 'n' tweets from two specified users, processing the text to remove noise such as stop words and irrelevant characters, and identifying the main topics each user tweets about, potentially using tools like Gensim for topic modeling. Participants are encouraged to devise their own methods for calculating a similarity score between the users' tweeting subjects. The challenge emphasizes learning and experimentation, with no strict guidelines or external libraries provided, and participants are invited to share their solutions at the end of the week for review.