What is the relation between isothermal process and its surrounding? 
In an isothermal process the temperature  of a system remains constant but may or may not be similar to temperature of surroundings

How is this possible?
 A: Isothermal processes can happen in the real-world because of insulation, very little heat exchange, or very little temperature change as the process happens.
For instance, most substances undergo an isothermal process when changing phase. You could even force some processes to become practically isothermal by cooling it as it happens. If you, say, had a gas in a cylinder, and expanded the volume in the cylinder, the gas will have more room to move around in, but the average velocity (or temperature!) of the gas remains the same.
A: I disagree with @PipperChip's answer (even though I upvoted it before realizing I did).
Insulation, together with small heat exchange, doesn't make a process isothermal, but adiabatic (that is, no net heat flow). Temperature is still free to vary, along with other parameters (and, in a pure substance, it must, or there's no process). An example is an isolated cylinder whose piston is pushed inwards: the air inside receives work, thus increasing its internal energy and, consequently, its temperature, without ever exchanging heat.
As far as I can see, the single most important example of isothermal process with temperature different from surroundings is phase change, which occurs at constant temperature (given constant pressure) in pure substances (and some mixtures). Often, the amounts of heat that can be absorved or lost isothermally during a phase change is very large. This leads to ubiquitous use, for example, in HVAC applications (heating, ventilating and air-conditioning), or, more prosaically, in your beer cooler.
