When you go to a website, your browser sends a request to the web server including a lot of information. This information might look something like this:
GET /questions/18070154/get-operating-system-info-with-php HTTP/1.1
Host: stackoverflow.com
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_4) AppleWebKit/537.36
(KHTML, like Gecko) Chrome/28.0.1500.95 Safari/537.36
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: en-us,en;q=0.5
Accept-Encoding: gzip,deflate,sdch
Accept-Charset: ISO-8859-1,utf-8;q=0.7,*;q=0.7
Keep-Alive: 300
Connection: keep-alive
Cookie: <cookie data removed>
Pragma: no-cache
Cache-Control: no-cache
These information are all used by the web server to determine how to handle the request; the preferred language and whether compression is allowed.
In PHP, all this information is stored in the $_SERVER array. To see what you're sending to a web server, create a new PHP file and print out everything from the array.
<pre><?php print_r($_SERVER); ?></pre>
This will give you a nice representation of everything that's being sent to the server, from where you can extract the desired information, e.g. $_SERVER['HTTP_USER_AGENT'] to get the operating system and browser.