Interrupt on Analog Port - ESP8266 w/ Arduino
Interrupts are a tricky concept to get, you have to be mindful of so many things (in bigger projects). 

Have a quick look on youtube for some tutorials, there are a heap out there. 

Having said all that, your code above isn't using interrupts at all. And you have these big delays, does the code work as published? 

I would suggest you rework the code into more of a state machine and have a single loop. ditch all the delays (except for your setup, that's fine) and go along the lines of:

setup

set a variable for current timer value and have a constant defined for your update interval

loop


read sensor (consider constantly reading, or reading it more often than the information is sent, and average it out)
anything on the serial port? 


go read it

check timer against old timer and interval
interval exceeded


send averaged value



using interrupts

You could use interrupts but the thing to consider is that they can be run AT ANY TIME. your code must be interrupt-able which whilst isn't too hard, needs special consideration in relation to delays, reading 16bit values, not having delays in the interrupt, status register changes, a whole host of others. 

There are two types of interrupt, those that are driven by a change in input and those that are time based. You don't really want the change in state on this one because you would normally want to monitor it constantly anyway, but it is certainly doable.

In both time based and external input, you would have the interrupt set a flag that gets acted upon in your main loop.

sorry for not providing more info at this time, screaming kids :(