Why is count(*) slow, when explain knows the answer?

Explain is using previously gathered statistics (used by the query optimizer). Doing a select count(*) reads EVERY data block.

Here's a cheap way to get an estimated row count:

SELECT table_rows
FROM information_schema.tables
WHERE table_name='planner_event';

Even if you did select count(id), it might still take a very long time, unless you have a secondary index on id (also assuming id is a PRIMARY KEY). Because all data (including Row Data) is stored in B-Tree indexes, performing a select count(PK_COLUMN) is still a considerable amount of IO (needs to reads all data pages). If you have a secondary index on the PK field, it will be able to perform less IO to perform a count.

Explain gets the number from some "statistics" that are used to estimate things for the Optimizer. That number can be far from correct -- I sometimes see it being more than a factor of 2 (higher or lower) than the exact value.

Performing the COUNT(*) on an InnoDB table must scan the table to avoid miscounting records that are busy being inserted/deleted by other connections but not yet "committed". Actually, it is good enough to do a full scan on some index, not necessarily the whole table (which contains the PRIMARY KEY).

How much RAM do you have? What is the value of innodb_buffer_pool_size? It might help if that were about 70% of RAM.