Hi,
The are a lot of way to do this.
One of the simplest is:

1. install php server,
2. write php script using shell_exec (http://php.net/manual/en/function.shell-exec.php) to execute your simple C program.

Thanks, darqoq.
I installed Armbian and I managed to connect to the board from the desktop in my own LAN using Putty. How can I connect from the outside? How should I install php server?

if you want to connect from outside LAN using :
- putty (you mean using ssh ?) you have to open port 22 on WAN
- web page you have install for example php server (or other web server that allows you to execute your code) and open port 80 on WAN

Thanks, I managed to connect to server.
Putty is SSH.
PHP server is also working.
The next question is how to make a measurement temperature once per minute.
What I want: 1) connect a temperature sensor to GPIOs (i would like to use DS18B20, but don't know how jet); 2) go to my web page form the outside and watch how the value of temperature changes (maybe add some diagram - temperature vs time).
For example, I have a measurement program temp_measure.c. How should it be launched once per minute? How the measured value should be transferred to my web page?
Thanks.