What is the meaning when it is said "Temperature of an Oxyacetylene Torch is 3500 degrees Celsius"? I don't think flame is anything but the product at that temperature but I am not sure. What exactly is flame? And I think the correct statement should be that the exothermic reaction here produces heat at such level that the temperature of the product gas reaches 3500 degrees. 
What will be the exact idea behind the statement?
Oxyacetylene is a mixture of acetylene (ethyne) and oxygen (not air). The mentioned temperature of about $T=3500\ \mathrm{^\circ C}$ is the adiabatic flame temperature for the combustion reaction of acetylene and oxygen.

An adiabatic process is one that occurs without transfer of heat. The adiabatic flame temperature is a theoretical temperature, which would be achieved in a combustion system in which there are no heat losses (e.g. no radiation losses from the flame). Note that this cannot be achieved in a real flame; therefore, adiabatic flame temperatures are calculated values.

The heat $Q$ released from the combustion reaction of acetylene and oxygen is the heat of combustion. If all of the energy released by this chemical reaction is used to increase the temperature $T$ of the products ($\ce{CO2}$ and $\ce{H2O}$) with no heat losses, the resulting adiabatic flame temperature can be calculated from the heat capacity $C$ of the products.

Hence, the adiabatic flame temperature represents the maximum possible theoretical temperature for a particular fuel/oxidant combustion.