What does it mean when MySQL is in the state "Sending data"?

In this state:

The thread is reading and processing rows for a SELECT statement, and sending data to the client.

Because operations occurring during this this state tend to perform large amounts of disk access (reads).

That's why it takes more time to complete and so is the longest-running state over the lifetime of a given query.

This is quite a misleading status. It should be called "reading and filtering data".

This means that MySQL has some data stored on the disk (or in memory) which is yet to be read and sent over. It may be the table itself, an index, a temporary table, a sorted output etc.

If you have a 1M records table (without an index) of which you need only one record, MySQL will still output the status as "sending data" while scanning the table, despite the fact it has not sent anything yet.

MySQL 8.0.17 and later: This state is no longer indicated separately, but rather is included in the Executing state.