TechDroidROOT:
Can't I use it as a shield for arduino Nano?
Yes, you could, but it's just much more cumbersome, and there's no reason whatsoever to do so.
Imagine an Arduino connected via USB to your computer. Let's say you want to receive messages over USB, and turn on/off relays.
You could connect a second Arduino to that first Arduino, and have the first Arduino receive messages, and the second turn on or off the relays. It would work of course, but it doesn't make any sense. The first Arduino can handle the relays perfectly fine, so adding the second Arduino is just a waste of hardware and (more importantly) time.
An ESP8266 is a microcontroller with WiFi built-in. As a microcontroller, it is many times more powerful than your standard Arduino, so it can perfectly turn on/off some relays while doing WiFi stuff at the same time.
Adding a second microcontroller is not a great solution.
If you find yourself needing more pins than the ESP-01 has available, get a board that breaks out all of the ESP8266's pins, like the WeMos D1 mini. Additional advantage: it has a USB interface to program it directly. It costs around €3, so that's really not the issue.
Alternatively, get a 74HC595 shift register to drive the relays using only 3 GPIO pins.
As for the software, take a look at this program with a web interface with slide switches to turn on/off the relays over WiFi.
Pieter