What is memory model in computer organization? I'm new to Computer Organization and even to this community. I didn't find anything which was simple, clear and up to the point. Any examples supporting the discussion is appreciated. I'm not looking for some text book answer.

Here's an example of my view to question: What is a Programmer's Model ?
Programmer's model shows what the CPU has available to a programmer for the execution of computer programs. 
It covers the CPU resources for execution of the CPU's instruction set.
(resources like state variables, AKA registers that can affect — or be affected by — the execution of instructions)

This programmer's model would NOT detail hardware, such as how the CPU's electronic circuitry works, 
how buses transport data or the I/O peripherals available.
i.e. The underlying details of how all of that is actually accomplished are hidden from the programmer.

In other words, the programmer's model would NOT cover functions that cannot be observed by CPU instructions. 
[EXCEPTION: those instructions trying to detect hardware operations, such as cache behavior, read/write variances because of varying bus delays etc are excluded]

So, similarly I wish to know what is a Memory Model ?
um I'm not sure if it is what you are looking for or not. I assume by memory model you mean the part in which we place input and do some calculation (like paper which we write something to remember and calculate).

The memory model depends on the definition of the model itself. In CS we have different kinds of computing model with different power.
One of the simplest one is Deterministic Finite Automata and informally its memory just contains an input string and nothing more.
One of the most powerful one is Turing machine that its memory is a infinite tape.
There are other models between these two such as PushDown Automata and Linear Bounded Automata where loosely speaking their memories contains stack of symbols and finite tape.

Also there are other models with same power as Turing machine, like two stack PDA, cellular automata and etc. 

So by how to define your computing model and program, your memory model details will be different.