How my Web server can send Web requests to my IoT thing?

CAUTION: A newbie about IoT concepts here!

I'll try to be short and explain what I want to do:

• Suppose that I already have connected my development board (be whatever you want; arduino, rpi, esp8266. The only requirement is to have a WiFi module on it) to my electric water heater.
• I return from my work and I want the water to be ready for my bath.
• The only thing I do is to visit (via my amazing smartphone) http://ift.tt/2eTEWuq and just press the button named activate!
• Bang! The development board has received a Web request from a User-agent, it activates the relay and my water heater is now turned on.

Can this be accomplished?

I suspect that I have to turn my dev board to a router in order to listen for Web requests (GET, POST, PUT). Is the WoT trying to solve this kind of things?

It is assumed that any authentication/authorization and security issues have been taken care of.