The weekly code challenge involves using Python and the Tweepy library to fetch and save tweets from specified Twitter handles into CSV files. Participants are guided to generate API keys, create a Tweepy API object, and define a class, `UserTweets`, which handles fetching tweets and saving them using namedtuples. The class constructor initializes with a Twitter handle and an optional `max_id` parameter, retrieves a set number of tweets, and saves them in a CSV format, allowing for iteration over the tweets. The challenge encourages users to participate by forking the repository and sharing feedback or code in the comments. Future challenges will build on this foundation, using NLP techniques to analyze tweet data for similarities across users.