The K-means algorithm partitions a dataset into K clusters by minimizing the variance within each cluster. It works by iteratively assigning data points to the nearest cluster centroid, then recalculating the centroids based on the new cluster members. The process repeats until the centroids stabilize.

Applications of K-means:

1. Customer Segmentation: Grouping customers based on purchasing behavior.
2. Image Compression: Reducing the number of colors in an image.
3. Anomaly Detection: Identifying unusual data points.
4. Document Clustering: Grouping similar documents for information retrieval.

Its simplicity and scalability make K-means popular for various clustering tasks.