Well, one way would be to e.g.. have a python script running to do the communications with the server, that then stores the value in a file on the SD card. That file can then be read by the code in the Arduino section, which can then do something with it (turn on LED, start motor or what not)
Sparkfun has an example doing the above, connecting to a mail server where you can look a bit at the code: https://learn.sparkfun.com/tutorials/galileo-unread-email-counter/the-arduino-sketch
I hope it helps you in the right direction!
/Thomas