What does the 'F' button and '2' button do (materials tab)?

Question

First, I know that clicking the '+' button on the right side of the material list makes an empty material slot, and after clicking the 'New'-button it adds a new material. But isn't it the same as just only clicking the 'New'-button (without clicking the '+' button first = empty slot)?

Second, I know that clicking the '+' button at the bottom next to the 'F'-button copies this material and makes it as a new node. Activating the 'F'-button will not delete unused material after closing the file.
What exactly does the '2' button do (when 'F' button activated)? Is it the same as just clicking the '+' button (at the bottom, next to 'F' button)? So what exactly does the 'F' button and '2' button do?

Answer 1

Some Theory

To understand how these buttons work, you first need to understand the concept of datablocks and users.

Everything in Blender is a datablock. An object is a datablock. A material is a datablock. A particle system is a datablock.

A user in blender, is something that uses a datablock. If you have a material, and you apply it to an object, that object's datablock becomes a user of that material. If you have a particle system applied to an object, that object's datablock becomes a user of it.

A datablock can have an infinite number of users. For example, there is no limit to how many times a material or a particle system can be applied to another object.

Blenders Garbage Disposal System

Before we can actually get into what this button does, I need to explain Blenders garbage disposal system.

Blender has a really neat, but somewhat annoying method of getting rid of datablocks.

Blender never deletes datablocks unless they have not users, and then, only when it's closed. So if you have a material that not objects use, and you close Blender, you lose that material.

The Fake User Button "F"

The way to stop this from happening is to use the "F" Button. The "F" stands for Fake User. This is exactly what it sounds like. It creates a fake user, so that the datablock always has at least one user, and doesn't get deleted by Blender when Blender is closed.

The "Number" Button

This also ties in with the whole idea of users. Basically, this displays the number of users this datablock has. If you click on it, it simply creates a duplicate of it, with 1 user (the datablock it's applied to).

Answer 2

First the "+" list buttons to add or remove a material slot, are there for when you have more then one material on the object. There is no way to add more then one new material with the large "New" button, if there is not already a material slot. (That is what the "+" button does.)

The "F" stands for Fake user, and as you know, when active will not be deleted.

When the "F" is active, the number of users for that data block is displayed on the left of the "F". Clicking the number (in your example a 2) does the exact same thing as clicking on the pulse button on the right side of the "F".

Answer 3

Datablocks

You will see these buttons on any datablock slot. A datablock is simply a set of parameters defining pretty much anything: materials, particle systems, textuers, sculpting brushes, node groups, even mesh data is stored in datablocks.

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Fake users

Clicking the F button will save the datablock (in this case the datablock is a material) when Blender closes, even if there are no users of the datablock. (As David said in his answer "F" stands for fake user.) If a datablock has no users (and no fake user) when Blender is closed, the datablock will be forgotten forever.

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Single-user copys

The 2 means that there are currently 2 users of the datablock (including the active object). Clicking on it will create a single-user copy, i.e. make a duplicate of the datablock and assign the duplicate to the active object in the active slot.