I found that there is a "fake user" button (with a
F icon) on object data tab in properties editor. What is the exact meaning of
users and its usage?
Blender organizes its data in datablocks. These are chunks of data (bits and bytes) that belong together, like all the settings of a material or the verts and faces of a mesh. When you give a mesh a material, this data isn't merged, but linked. You tell Blender: whenever you use mesh X, display it with material Y.
When a material is linked to something, it has a user. Another datablock that uses this material. When a material is used by a lot of objects or meshes, it has many users, displayed by the number to the right of it's name.
That way you can have a thousand objects all using the same mesh, which takes up less memory and enables you to edit one mesh and affect all linked objects simultaneously.
Fake users are a way to keep a material alive even if no object or mesh uses this material. If a datablock has no users, it will not be saved when you save the file in order to decrease file size. Think of it as some kind of garbage collection. However, the fake user takes care of this problem.
To illustrate that, I have resurrected Blender 2.28 because it has a view called OOPS schematic that shows the linking very well. Below, you have four objects all linking to one Suzanne mesh. I'm in the edit mode of the upper left Suzie and mess with her ears. Since all four objects use the same mesh, all objects are changed simultaneously.
One easily overlooked feature is copying lamps with altD. All the lamps then share the same data. This way you can change every lamp's brightness in one go. Think of a row of street lamps.
Users refer to parts of blender that are using that item. For example an image could be used as a reference image and also used in a texture so it's users would be listed as 2 because two parts of blender are using it.
The fake user option is there to prevent blender from removing that data from the blend file when the file is closed. When closing, Blender will look through parts of the blend file and if something isn't being used (it has zero users) it will be removed from the blend file. Pressing 'F' ensures that blender will keep the data even if it isn't being used, because you might want to use the data at a later date.
In terms of 'Object Data', this means that the vertices that make up the object, the shape keys, UV maps and vertex colours will be shared between 2 different objects. This can be used to create instances of an object so that editing one will update the other because they are linked.
Editing a cube that was sharing object data would update the other cube at the same time regardless of their position, scale or rotation in the scene.
Users means the number of datablocks that have refernces to the datablock that shows the number of references. To avoid that e.g. that a material will be removed when the .blend file is saved, a fake user can be added, otherwise a non referenced material would be discarded.
See also the docs on Users and Fake User