The Sentiment Analysis API is used to analyze the tone and sentiment of comments on Twitter feeds, allowing users to compare political candidates or make investment decisions by identifying trends over time. The API provides a simple usage process, returning a score, judgment, and breakdown by keyword in JSON format. To perform this analysis, users can sign up for a free account at RapidAPI.com and connect to the Sentiment Analysis API using their preferred programming language. A list of tweets from a given Twitter handle is generated using TwitRSS.me, which parses Twitter feeds into RSS format, and then looped through to analyze each tweet's sentiment using the API. The analysis results in statistics such as average sentiment scores and most positive/negative tweets, providing insights into the tone and sentiment of the user's tweets over time.