Firing Pin Block

What is the purpose of a firing pin block?
It's to prevent the firing pin from striking the primer if the firearm was ever dropped.
Employing a firing pin block means that even if your gun is loaded and all the safeties are OFF, dropping the firearm will not cause an accidental discharge.

What are the kinds of blocks?
Colt's original design is just called a firing pin block. It is disengaged from pulling the trigger as shown:

In a clone, such as Kimber, Sig, etc., the firing pin's block is called the "Schwartz Safety" and is affected by engaging the grip safety as shown here in a Series II illustration:

"Series 80" and "Series II" mean the same thing; firing pin block.
"Series 70" and "Pre-series II" mean the same thing; NO firing pin block.
How can you tell the difference if that isn't stamped on the gun?

If the name doesn't denote that it's a series 80 (Kimber's II) or a series 70 (Kimber's pre-series II), you can tell by locking the slide back and looking up underneath.
Here's my Kimber Ultra Carry II... Note that in the grooves on the RIGHT side, there's a round plunger. This is indicative of the firing pin block.

Here's my Rock Island Armory, a copy of Colt's series 70...note the lack of that circular plunger in the right side groove - No firing pin block.