It is a vast area. The major areas include mechanical, thermal, dielectric properties. Some properties are intrinsic and some are extrinsic. You have to explore how the material is being used.

May be my question is in ambiguous form . is it the endpoint at where we cannot provide the answer of why?

Hmm, not sure to understand your question. The term "property" does not point to a limitation. It is a term indicating any characteristic "behavior".

Take a piece of iron: the fact that it weighs about 7.4g per cubic centimeter is a property (mass density) of iron. Other materials will in general have different values for this property.

Electrical conductivity is another property. You may just want to know a numerical value, but you may also want to understand what the mechanisms are that lead to this value. All these things belong to the set of properties of the material.

Properties are what lets us describe materials. It is a very broad term. There may be properties which we don't yet understand (e.g. mechanism of superconductivity in some oxide materials). This then, is a momentary limit of scientific understanding.

Thank you for your nice answer.It is clear that property gives the identification of something. However , still i got some confusion about the complete definition of property. For example , water get the boiling temperature 100 degree Celsius, it's obviously a distinguishing parameter to identify this. In the case when question arise , why it shows this ? then may be there is some reason . but at a point (further asking of why ...why...) we cannot provide any convincing answer. Then we define that it's the property of so and so . So , I think property pertains both meaning of identification and limitation of knowledge of that material. Am I correct?

In my view the term "property" stands in its own right, regardless of whether we are able to justify its existence or value via some principles or laws which we regard as being more fundamental - or not.

Occurrence of temperature values of phase transitions and the physical states associated with the transitions are actually an excellent example.

Take superconductors for example:

being superconducting (at sufficiently low temperature) is certainly a property of Hg. The value of T_C is another, certainly related one. We could establish the order of the phase transition from thermodynamic measurements as yet another property, without having a clue how the mechanism of superconductivity works. Later, we can find out that there are type I and type II superconductors (being one of them is a property), which categorizes two classes of behaviour of superconductors in magnetic fields. In the end it took 50years or so from the discovery of superconductivity to the completion of a first working theory (= possible understanding) of it.

Surely property is not related to knowledge limits. If we remove humans and thus their knowledge, this would not lead to elimination of properties.

Any property of just about any system would have to be related to the concept of causality - it is something that defines the response of any system to the effects of known stimuli. Thus, properties set the boundaries in relation to the effects and their physical causes.

I got it, but what about the properties (result) of phenomenon. For example, result of heat transfer is to transfer heat from higher to lower.However it does not comply in connection of the result of radiation heat transfer from sun to earth. Earth gets higher temperature than clouds. Why?

Because the earth and cloud materials have different combinations of various properties relevant to heat transfer phenomena - for example, transparency to radiant heat, the ability to absorb or scatter or re-radiate that heat, as well as surrounding environments (water, earth, air or rarified atmospheric gases) again possessing different properties with respect to radiation propagation and absorption. Thanks for this very interesting question.

This is a philosophical question rather than a science based one. Nothing wrong with this as many new developments in science originated in philosophy. Material system here would mean the presence of a system based only on the accepted concepts of physics meaning anything made up of matter and energy and the presence of physical forces.

Properties of any materials are those which can specify the material and help us identify that among any other materials. That will be the most basic definition, I suppose.

But our scientific community had changed the definition whenever nedded, accordingly. e.g. We are only concerned about the properties that actually effect our experiments and don't bother about others.