Question: This letter "$\varepsilon$" is called epsilon right ? What does it signify in mathematics ?

Answer: 
The greek letter epsilon, written $\epsilon$ or $\varepsilon$, is just another variable, like $x$, $n$ or $T$.

Conventionally it's used to denote a small quantity, like an error, or perhaps a term which will be taken to zero in some limit.

It's possible that you are confusing it with the set membership symbol $\in$, which is something different. When you see $x\in X$ it means that $X$ is a set, and $x$ is a member of the set. For example,

$$1\in \{1,2,3\}$$

is true, but

$$4\in\{1,2,3\}$$

is false.
Here's a not too well-known instance of the use of $\varepsilon$ in mathematics:

One somewhat well-known transformation for accelerating the convergence of a sequence is the [Shanks transformation](http://en.wikipedia.org/wiki/Shanks_transformation) (after [Daniel Shanks](http://en.wikipedia.org/wiki/Daniel_Shanks), who is probably more well-known for his number-theoretic contributions). What the Shanks transformation essentially does, assuming that the sequence given is a sequence of Taylor polynomials evaluated at a certain argument, is to transform this sequence of Taylor approximants into a sequence of [Padé rational approximants](http://en.wikipedia.org/wiki/Pad%C3%A9_approximant).

The Shanks transformation of a sequence can be expressed as a ratio of two determinants, but there is a more efficient realization of this, the [Wynn $\varepsilon$ algorithm](http://dx.doi.org/10.1090/S0025-5718-1956-0084056-6):

$$\varepsilon\_{k+1}^{(n)}=\varepsilon\_{k-1}^{(n+1)}+\frac1{\varepsilon\_{k}^{(n+1)}-\varepsilon\_k^{(n)}}$$

where $\varepsilon\_0^{(n)}=S\_n$ is the sequence to be transformed.