What is meant by "Big Bang" in expressions like "$10^{-36}$ seconds after the Big Bang"? Sometimes I find expressions like "The inflationary epoch lasted from $10^{−36}$ seconds after the conjectured Big Bang singularity [...]". What is meant by "the Big Bang" in this context?
I understand "Big Bang theory" as the whole explanation of how the universe evolved form a very dense and hot state. Isn't "the Big Bang" the process of expansion rather than a singular event? If not, what should I understand by "Big Bang"?
 A: The Big Bang was a singularity. By analogy, the function $f(x)=1/\sqrt{x}$ has a domain $(0,\infty)$, which doesn't include $x=0$ because the function misbehaves there. The Big Bang singularity is technically not considered an "event" because it's not a point or set of points that we include on the spacetime manifold.
So time since the big bang means the upper bound on the time measured by any clock that has always been at rest relative to the Hubble flow.
A: The expansion event we call the "Big Bang" had a beginning. Depending on the context, that term can either refer to its beginning point (or very close to it) in time, or to the first few minutes of it during which all the hydrogen and helium in the early universe was formed. 
A: I think it is just slight misunderstanding. 
Big bang itself indeed denote the moment of singularity in the universe.
Big bang theory is a theory that describe the evolution of the universe assuming there is such moment of singularity in the beginning of its evolution.
Compare for example to the steady-state theory for which the universe is expanding but retain a constant finite density, hence no singularity.
