Can I control a Arduino from an apache server?
If you attach a 'network adapter' to the Arduino, you can start a TCP server on Arduino. The server, a telnet server or a web server will listen for commands  sent from computer. In case of web server, you can send commands from web browser too. Other option is to use UDP communication. Arduino can listen UDP.

The options for the network are Ethernet or WiFi. Both are in form of shields or modules. For Ethernet Wiznet 5100 and 5500 chips are best supported and for WiFi the esp8266 is the common option.