Need some expert comments on it : What exactly is getting expanded in Big Bang model?
Is space like a elastic material which can be stretched and inflated? Or, new space is getting created with expansion? How expansion happens as per general relativity and Big Bang model?
The contents of the universe are expanding. These could include matter, radiation, fields, or whatever. Within the context of the simplest descriptions of cosmology, all of these are modeled as perfect fluids.
In principle, you can construct a cosmological model with only contents that cannot meaningfully expand, like empty space (the Milne model) or a cosmological constant (de Sitter space). However, these models both admit static descriptions: the Milne model is equivalent to Minkowski space while de Sitter space can be expressed in a manifestly static form. So there is not a clear physical sense in which they are expanding. Cosmic expansion is only physical to the extent that the stuff in the universe is expanding.
When considering an expanding spacetime, one usually works with the metric
$$c^2\text d\tau^2=c^2\text dt^2-a^2(t)(\text dx^2+\text dy^2+\text dz^2),$$
and consider $a(t)$ to be increasing with time. This is the FLRW model of an expanding/contracting Universe.
If you look at the proper distance between two events (say, $x^\mu=(0,0,0,0)$ and $y^\mu=(0,1,0,0)$), it is clear that the proper distance between them is directly proportional to $a^2(t)$. So, as $a(t)$ increases over time, those two points "appear" to be moving away from each other at a rate proportional to their speed, even though their coordinate distance is constant.
In this sense, all three of the spatial dimensions are getting "expanded" in some sense, insofar as the proper distances along them are increasing. This can sort of be visualized as the lengths of unit meter sticks in each direction getting shorter proportional to $a^2(t)$, and thus more meter sticks are required to fit between any two given points, and thus the measured distance between those points increases as $a(t)$ does.
