See if this helps with the understanding:

Using this data:
A1: DUCK
B1: DUCK
C1: (blank)
D1: CAT

and the formula =SUMPRODUCT((A1:D1<>"")/COUNTIF(A1:D1,A1:D1&""))

The (A1:D1<>"") part tests if each cell in A1:D1 is not blank. Each
non-blank returns a 1, each blank returns a zero. (Actually, it returns TRUE
and FALSE, but Excel converts them to 1's and 0's)
Consequently, the example data would return this array: 1,1,0,1

Next, the COUNTIF(A1:D1,A1:D1&"") section counts how many times it finds
each cell's value in the range A1:D1.
Our data would return the array: 2,2,1,1

So the resulting array divisions would match the items from the first array
with the items in the second array to get: 1/2, 1/2, 0/2, 1/1

The SUMPRODUCT function adds all of those values and is only really
necessary in this example to force Excel to perform array calculations.   In
this case, the total equals 2 unique items.

You could skip the SUMPRODUCT function and use this formula instead:
=SUM((A1:D1<>"")/COUNTIF(A1:D1,A1:D1&""))
...but you'd need to confirm that array formula by holding down the [Ctrl]
and [Shift] keys when you press [Enter]. For many people, that's too obscure
a combination to remember only occaissionally.  Hence, I generally prefer the
SUMPRODUCT function approach.

I hope that helps?

***********
Regards,
Ron