What's the purpose of Kafka's key/value pair-based messaging?

Kafka uses the abstraction of a distributed log that consists of partitions. Splitting a log into partitions allows to scale-out the system.

Keys are used to determine the partition within a log to which a message get's appended to. While the value is the actual payload of the message. The examples are actually not very "good" with this regard; usually you would have a complex type as value (like a tuple-type or a JSON or similar) and you would extract one field as key.

See: http://kafka.apache.org/intro#intro_topics and http://kafka.apache.org/intro#intro_producers

In general the key and/or value can be null, too. If the key is null a random partition will the selected. If the value is null it can have special "delete" semantics in case you enable log-compaction instead of log-retention policy for a topic (http://kafka.apache.org/documentation#compaction).

Late addition... Specifying the key so that all messages on the same key go to the same partition is very important for proper ordering of message processing if you will have multiple consumers in a consumer group on a topic.

Without a key, two messages on the same key could go to different partitions and be processed by different consumers in the group out of order.