What is the function of "hamon"?
I am curious about the correct usage of this word. 

Would you please give me an explanation as well as a few examples?

Kheili mamnoonam!

It means "That" . As a sample: 

Hamoon aadam = That person

Hamoon rooz = That day

Hamoon moghe = at that moment.

it usually refers to a particular time or thing. 

and sometimes it is used this way:

faghat hamoon bood? = was it all?

this one is a little complicated ;)