How does it compare to Apache Kafka? (I haven't used either.)
Storm is distributed stream processing.
The two work together very well. Often, a server will publish messages to Kafka (or another queue), which are then read and processed by Storm.
http://www.slideshare.net/gschmutz/kafka-andstromeventproces...
Slides 42 and 43 describe an architecture with all three ... hadoop, storm and kafka. Seems like a beast and I don't have applications but pretty cool combo of technologies.
https://github.com/apache/storm/tree/master/external/storm-k...