Burning fuel leaves behind some residue.  This can build up around the
nozzles of the injectors and either restrict flow or change the spray
pattern enough to effect performance.  They temporarily disable the fuel
supply from the tank and run the motor off a cleaning solution which removes
the residue.

Two possibilities that have happened to me....

1) I have had several instances of filling the gas tank in my 92
explorer and then having the same sort of starting issue you describe.
What happens is that the gas is on the far end of the range for
volatility and doesn't like to vaporize.  So until I burn up that tank
it takes a lot more cranking.  Then fill it up again and the problem
goes away.  The same thing often happens if you put premium gas in a
car designed to run on regular.  Premium has a lower volatility and it
makes it harder to start the car.  The automakers have gotten so many
complaints of this kind of hard starting that they have issues TSB's
to the dealers advising them to tell the customers to stop putting
premium gas in because it makes it hard to start the car.

2) On my 99 mustang GT it suddenly developed the same sort of change
in how it started, going from starting in about half a second to
taking several seconds.  It was under warranty and I took it in. First
time they could not find anything in particular but went ahead and
replaced teh cam position sensor.  That did not help.  I took in back
in a month or so and when I got it back they said it was one of the
stranger things they had come across.  Turned out the Alternator was
"bad" even though it had still be working well enough to keep the
battery up.  The bad alternator was somehow causing low voltage or
something during startup and that was creating issues with the engine
computer resulting in the hard starting.  They replaced the alternator
and it was back to starting up properly again.