It's the integrator error tolerance. If you use dassl with a low (1e-3) tolerance you get faster simulation but a bigger allowed error.
Note that some models simulate faster with a higher tolerance (1e-6 or 1e-7) because it helps getting better guesses for non-linear systems.

Note that the error is accumulated. If you want a maximum error of 1e-3 you might have to use a tolerance of 1e-5, etc.

Is the tolerance signify :

     |  ( x(i) - x(i+1) ) /  x(i+1) | < tolerance ?

Where x is an unknown and i represent the number of the iteration : x( i ) is the value of an unknown x at the iteration i.

It's an error estimate of derivatives only. The code does not specify how the local error is estimated. You can check http://www.netlib.no/netlib/ode/ddasrt.f

Thanks for the fast reply. One more question. Will changing the tolerance values affect the value of the results obtained?

Of course. That's the whole point of it.